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<*• 

JtioK          ' 


w  «  wondrous  strange" 


A  ROMANCE 
OF  MANY  DIMENSIONS 


UN  BLAH* 


SSI 

// 


•7^? 


' 


I    [ABBOT  (E.)]  Flatland  :    a  Romance  of 
original  parchment  wrappers,  VERY  SCAR< 


by  A  Square,  sm.  410., 
1884 


FLATLAND 

A  Romance  of  Many  Dimensions 


FLATLAND 


A  Romance  of  Many  Dimensions 


With  Illustrations 
by   the   Author,  A  SQUARE 


"  Fie,  fie,  how  franticly  1  square  my  talk!' 


LONDON 
SEELEY  &f  Co.,  46,  47   &r  48,   ESSEX   STREET,  STRAND 

(Late  15/54  FLEET  STREET) 
1884 


LONDON  : 

R.  CLAY,  SONS,  AND  TAYLOR, 

BREAD   STREET   HILL. 


To 

The  Inhabitants  of  SPACE  IN  GENERAL 
And    H.    C.    IN    PARTICULAR 

This  Work  is  Dedicated 
By  a  Humble  Native  of  Flatland 

In  the  Hope  that 
Even  as  he  was  Initiated  into   the  Mysteries 

Of  THREE  Dimensions 
Having   been   previously  conversant 

With  ONLY  Two 
So  the  Citizens  of  that  Celestial   Region 

May  aspire  yet  higher  and  higher 
To  the  Secrets  of  FOUR  FIVE  OR  EVEN  Six  Dimensions 

Thereby  contributing 
To  the  Enlargement  of  THE   IMAGINATION 

And  the  possible   Development 

Of  that  most  rare  and  excellent  Gift  of  MODESTY 

Among  the  Superior  Races 

Of   SOLID  HUMANITY 


CONTENTS 

PART  I 

THIS    WORLD 

Section 

1  Of  the  Nature  of  Flatland 

2  Of  the  Climate  and  Houses  in  Flatland 

3  Concerning  the  Inhabitants  of  Flatland 

4  Concerning  the  Women 

5  Of  our  Methods  of  Recognizing  one  another 

6  Of  Recognition  by  Sight 

7  Concerning  Irregular  Figures 

8  Of  the  Ancient  Practice  of  Painting 

9  Of  the  Universal  Colour  Bill 

10  Of  the  Suppression  of  the  Chromatic  Sedition 

1 1  Concerning  our  Priests 

12  Of  the  Doctrine  of  our  Priests 


viii  Contents 


Section 

13  How  1  had  a  Vision  of  Lineland 

14  How  in  my   Vision  I  endeavoured  to  explain  the  nature  of  Flatland,  but 

could  not 

15  Concerning  a  Stranger  from  Spaceland 

1 6  How  the  Stranger  vainly  endeavoured  to  reveal  to  me  in  words  the  mysteries 

of  Spaceland 

1 7  How  the  Sphere,  having  in  vain  tried  words ;  resorted  to  deeds 

1 8  How  I  came  to  Spaceland  and  what  I  saw  there 

19  How,  though  the  Sphere  showed  me  other  mysteries  of  Spaceland,  I  still 

desired  more ;  and  what  came  of  it 

20  How  the  Sphere  encouraged  me  in  a  Vision 

2 1  How  I  tried  to  teach  the  Theory  of  Three  Dimensions  to  my  Grandson,  and 

with  what  success 

22  How  I  then  tried  to  diffuse  the  Theory  of  Three  Dimensions  by  other  means, 

and  of  the  result 


PART  1 


"Be  -patient,  for  the  world  is  broad  and  wide" 


FLATLAND 

PART  I 
THIS  WORLD 

§  i. — Of  the  Nature  of  Flat  land. 

I  CALL  our  world  Flatland,  not  because  we  call  it  so,  but  to  make 
its  nature  clearer  to  you,  my  happy  readers,  who  are  privileged  to  live 
in  Space. 

Imagine  a  vast  sheet  of  paper  on  which  straight  Lines,  Triangles, 
Squares,  Pentagons,  Hexagons,  and  other  figures,  instead  of  remaining 
fixed  in  their  places,  move  freely  about,  on  or  in  the  surface,  but  without 
the  power  of  rising  above  or  sinking  below  it,  very  much  like  shadows 
— only  hard  and  with  luminous  edges — and  you  will  then  have  a  pretty 
correct  notion  of  my  country  and  countrymen.  Alas,  a  few  years  ago, 
I  should  have  said  "  my  universe  "  :  but  now  my  mind  has  been  opened 
to  higher  views  of  things. 

In  such  a  country,  you  will  perceive  at  once  that  it  is  impossible  that 
there  should  be  anything  of  what  you.  call  a  "  solid  "  kind  ;  but  I  dare  say 
you  will  suppose  that  we  could  at  least  distinguish  by  sight  the  Triangles 
Squares  and  other  figures  moving  about  as  I  have  described  them.  On 
the  contrary,  we  could  see  nothing  of  the  kind,  not  at  least  so  as  to 


4  Flatland 

distinguish  one  figure  from  another.  Nothing  was  visible,  nor  could  be 
visible,  to  us,  except  straight  Lines;  and  the  necessity  of  this  I  will 
speedily  demonstrate. 

Place  a  penny  on  the  middle  of  one  of  your  tables   in    Space ;  and 
leaning  over  it,  look  down  upon  it.     It  will  appear  a  circle. 

But   now,  drawing  back  to   the   edge  of  the  table,  gradually  lower 
your  eye  (thus  bringing  yourself  more   and  more  into  the  condition  of 
the  inhabitants  of  Flatland),  and  you  will  find  the  penny  becoming  more 
and  more  oval  to  your  view ;  and  at  last  when   you  have   placed   your 
eye  exactly  on   the   edge   of   the   table   (so   that   you   are,   as   it   were, 
actually  a  Flatland  citizen)  the  penny   will  then  have  ceased  to  appear 
oval  at  all,  and  will  have  become,  so  far  as  you  can  see,  a  straight  line. 
The  same  thing  would  happen  if  you  were  to  treat  in  the  same  way  a 
Triangle,  or  Square,  or  any  other  figure  cut  out  of  pasteboard.     As  soon 
as  you  look  at  it  with  your  eye  on  the  edge  of 
the  table,  you  will  find  that  it  ceases  to  appear 
to  you   a  figure,  and  that  it  becomes  in  appear- 
ance   a    straight    line.       Take    for    example    an 
equilateral   Triangle — who    represents  with   us   a 
Tradesman    of    the    respectable    class.      Fig.    I 
represents  the  Tradesman  as  you  would  see  him 

while   you   were   bending   over  him   from  above ; 

•(2) 

figs.  2   and    3    represent  the  Tradesman,   as  you 

would   see  him   if    your  eye  were  close    to  the 

level,  or  all  but  on   the  level   of  the  table;  and 

(3) 

if  your  eye  were  quite  on  the  level  of  the  table 

(and  that  is   how  we  see   him   in   Flatland)  you 
would  see  nothing  but   a  straight  line. 

When  I  was  in  Spaceland  I  heard  that  your  sailors  have  very  similar 
experiences  while  they  traverse  your  seas  and  discern  some  distant  island 


Flatland  5 

or  coast  lying  on  the  horizon.  The  far-off  land  may  have  bays,  forelands, 
angles  in  and  out  to  any  number  and  extent ;  yet  at  a  distance  you  see 
none  of  these  (unless  indeed  your  sun  shines  bright  upon  them  revealing 
the  projections  and  retirements  by  means  of  light  and  shade),  nothing  but 
a  grey  unbroken  line  upon  the  water. 

Well,  that  is  just  what  we  see  when  one  of  our  triangular  or  other 
acquaintances  comes  towards  us  in  Flatland.  As  there  is  neither  sun 
with  us,  nor  any  light  of  such  a  kind  as  to  make  shadows,  we  have  none 
of  the  helps  to  the  sight  that  you  have  in  Spaceland.  If  our  friend 
comes  close  to  us  we  see  his  line  becomes  larger  ;  if  he  leaves  us  it 
becomes  smaller :  but  still  he  looks  like  a  straight  line ;  be  he  a 
Triangle,  Square,  Pentagon,  Hexagon,  Circle,  what  you  will — a  straight 
Line  he  looks  and  nothing  else. 

You  may  perhaps  ask  how  under  these  disadvantageous  circumstances 
we  are  able  to  distinguish  our  friends  from  one  another:  but  the  answer 
to  this  very  natural  question  will  be  more  fitly  and  easily  given  when  I 
come  to  describe  the  inhabitants  of  Flatland.  For  the  present  let  me 
defer  this  subject,  and  say  a  word  or  two  about  the  climate  and  houses  in 
our  country. 

§  2. — Of  the  climate  ana  houses  in  Flatland. 

As  with  you,  so  also  with  us,  there  are  four  points  of  the  compass 
North,  South,  East,  and  West. 

There  being  no  sun  nor  other  heavenly  bodies,  it  is  impossible  for  us  to 
determine  the  North  in  the  usual  way ;  but  we  have  a  method  of  our  own.  By 
a  Law  of  Nature  with  us,  there  is  a  constant  attraction  to  the  South  ;  and, 
although  in  temperate  climates  this  is  very  slight — so  that  even  a  Woman 
in  reasonable  health  can  journey  several  furlongs  northward  without  much 
difficulty — yet  the  hampering  effect  of  the  southward  attraction  is  quite 
sufficient  to  serve  as  a  compass  in  most  parts  of  our  earth.  Moreover 


6  Flatland 

the  rain  (which  falls  at  stated  intervals)  coming  always  from  the  North,  is 
an  additional  assistance ;  and  in  the  towns  we  have  the  guidance  of  the 
houses,  which  of  course  have  their  side-walls  running  for  the  most  part 
North  and  South,  so  that  the  roofs  may  keep  off  the  rain  from  the 
North.  In  the  country,  where  there  are  no  houses,  the  trunks  of  the 
trees  serve  as  some  sort  of  guide.  Altogether,  we  have  not  so  much 
difficulty  as  might  be  expected  in  determining  our  bearings. 

Yet  in  our  more  temperate  regions,  in  which  the  southward  attraction 
is  hardly  felt,  walking  sometimes  in  a  perfectly  desolate  plain  where  there 
have  been  no  houses  nor  trees  to  guide  me,  I  have  been  occasionally 
compelled  to  remain  stationary  for  hours  together,  waiting  till  the  rain  came 
before  continuing  my  journey.  On  the  weak  and  aged,  and  especially  on 
delicate  Females,  the  force  of  attraction  tells  much  more  heavily  than 
on  the  robust  of  the  Male  Sex,  so  that  it  is  a  point  of  breeding,  if  you 
meet  a  Lady  in  the  street,  always  to  give  her  the  North  side  of  the  way 
— by  no  means  an  easy  thing  to  do  always  at  short  notice  when 
you  are  in  rude  health  and  in  a  climate  where  it  is  difficult  to  tell  your 
North  from  your  South. 

Windows  there  are  none  in  our  houses:  for  the  light  comes  to  us 
alike  in  our  homes  and  out  of  them,  by  day  and  by  night,  equally  at 
all  times  and  in  all  places,  whence  we  know  not.  It  was  in  old  days, 
with  our  learned  men,  an  interesting  and  oft-investigated  question, 
What  is  the  origin  of  light ;  and  the  solution  of  it  has  been  repeatedly 
attempted,  with  no  other  result  than  to  crowd  our  lunatic  asylums 
with  the  would-be  solvers.  Hence,  after  fruitless  attempts  to  suppress 
such  investigations  indirectly  by  making  them  liable  to  a  heavy  tax, 
the  Legislature,  in  comparatively  recent  times,  absolutely  prohibited 
them.  I,  alas  I  alone  in  Flatland — know  now  only  too  well  the  true 
solution  of  this  mysterious  problem  ;  but  my  knowledge  cannot  be  made 
intelligible  to  a  single  one  of  my  countrymen  ;  and  I  am  mocked  at — I, 


Flatland 


the  sole  possessor  of  the  truths  of  Space  and  of  the  theory  of  the 
introduction  of  Light  from  the  world  of  Three  Dimensions — as  if  I  were 
the  maddest  of  the  mad !  But  a  truce  to  these  painful  digressions  : 
let  me  return  to  our  houses. 

The  most  common  form  for  the  construction  of  a  house  is  five-sided 
or    pentagonal,    as    in   the  annexed    figure.      The  two    Northern    sides 
RO,    OF,  constitute    the    roof,    and 
for  the  most  part  have  no  doors ;  on 
the  East   is  a    small    door    for    the 
Women  ;  on  the  West  a  much  larger 
one  for  the  Men  ;  the  South  side  or 
floor  is  usually  doorless. 

Square  and  triangular  houses  are 
not  allowed,  and  for  this  reason. 
The  angles  of  a  Square  (and  still 
more  those  of  an  equilateral  Triangle) 
being  much  more  pointed  than  those 

of  a  Pentagon,  and  the  lines  of  inanimate  objects  (such  as  houses) 
being  dimmer  than  the  lines  of  Men  and  Women,  it  follows  that  there 
is  no  little  danger  lest  the  points  of  a  square  or  triangular  house 
residence  might  do  serious  injury  to  an  inconsiderate  or  perhaps  absent- 
minded  traveller  suddenly  running  against  them :  and  therefore,  as 
early  as  the  eleventh  century  of  our  era,  triangular  houses  were 
universally  forbidden  by  Law,  the  only  exceptions  being  fortifications, 
powder-magazines,  barracks,  and  other  state  buildings,  which  it  is  not 
desirable  that  the  general  public  should  approach  without  circumspection. 

At  this  period,  square  houses  were  still  everywhere  permitted,  though 
discouraged  by  a  special  tax.  But,  about  three  centuries  afterwards,  the 
Law  decided  that  in  all  towns  containing  a  population  above  ten  thousand, 
the  angle  of  a  Pentagon  was  the  smallest  house-angle  that  could  be 


8  Flatland 

allowed  consistently  with  the  public  safety.  The  good  sense  of  the 
community  has  seconded  the  efforts  of  the  Legislature  ;  and  now,  even 
in  the  country,  the  pentagonal  construction  has  superseded  every  other. 
It  is  only  now  and  then  in  some  very  remote  and  backward  agricultural 
district  that  an  antiquarian  may  still  discover  a  square  house. 

§  3. — Concerning   the  Inhabitants  of  Flatland. 

The  greatest  length  or  breadth  of  a  full-grown  inhabitant  of  Flatland 
may  be  estimated  at  about  eleven  of  ryour  inches.  Twelve  inches  may 
be  regarded  as  a  maximum. 

Our  Women  are  Straight  Lines. 

Our  Soldiers  and  Lowest  Classes  of  Workmen  are  Triangles  with  two 
equal  sides,  each  about  eleven  inches  long,  and  a  base  or  third  side  so 
short  (often  not  exceeding  half  an  inch)  that  they  form  at  their  vertices 
a  very  sharp  and  formidable  angle.  Indeed  when  their  bases  are  of  the 
most  degraded  type  (not  more  than  the  eighth  part  of  an  inch  in  size), 
they  can  hardly  be  distinguished  from  Straight  Lines  or  Women  ;  so 
extremely  pointed  are  their  vertices.  With  us,  as  with  you,  these  Triangles 
are  distinguished  from  others  by  being  called  Isosceles  ;  and  by  this 
name  I  shall  refer  to  them  in  the  following  pages. 

Our  Middle  Class  consists  of  Equilateral  or  Equal-sided  Triangles. 

Our  Professional  Men  and  Gentlemen  are  Squares  (to  which  class 
I  myself  belong)  and  Five-sided  figures  or  Pentagons. 

Next  above  these  come  the  Nobility,  of  whom  there  are  several 
degrees,  beginning  at  Six-sided  Figures,  or  Hexagons,  and  from  thence 
rising  in  the  number  of  their  sides  till  they  receive  the  honourable  title 
of  Polygonal,  or  many-sided.  Finally  when  the  number  of  the  sides 
becomes  so  numerous,  and  the  sides  themselves  so  small,  that  the  figure 
cannot  be  distinguished  from  a  circle,  he  is  included  in  the  Circular  or 
Priestly  order ;  and  this  is  the  highest  class  of  all. 


It  is  a  Law  of  Nature  with  us  that  a  male  child  shall  have  one  more 
side  than  his  father,  so  that  each  generation  shall  rise  (as  a  rule)  one  step 
in  the  scale  of  development  and  nobility.  Thus  the  son  of  a  Square 
is  a  Pentagon  ;  the  son  of  a  Pentagon,  a  Hexagon ;  and  so  on. 

But  this  rule  applies  not  always  to  the  Tradesmen,  and  still  less 
often  to  the  Soldiers,  and  to  the  Workmen;  who  indeed  can  hardly  be 
said  to  deserve  the  name  of  human  Figures,  since  they  have  not  all  their 
sides  equal.  With  them  therefore  the  Law  of  Nature  does  not  hold ; 
and  the  son  of  an  Isosceles  (i.e.  a  Triangle  with  two  sides  equal)  remains 
Isosceles  still.  Nevertheless,  all  hope  is  not  shut  out,  even  from  the 
Isosceles,  that  his  posterity  may  ultimately  rise :  above  his  degraded 
condition.  For,  after  a  long  series  of  military  successes,  or  diligent 
and  skilful  labours,  it  is  generally  found  that  the  more  intelligent  among 
the  Artisan  and  Soldier  classes  manifest  a  slight  increase  of  their  third  side 
or  base,  and  a  shrinkage  of  the  two  other  sides.  Intermarriages  (arranged 
by  the^  Priests)  between  the  sons  and  daughters  of  these  more  intellectual 
members  of  the  lower  classes  generally  result  in  an  offspring  approxi- 
mating still  more  to  the  type  of  the  Equal-sided  Triangle. 

Rarely — in  proportion  to  the  vast  number  of  Isosceles  births— is  a 
genuine  and  certifiable  Equal-sided  Triangle  produced  from  Isosceles 
parents.1  Such  a  birth  requires,  as  its  antecedents,  not  only  a  series  of 
carefully  arranged  intermarriages,  but  also  a  long-continued  exercise  of 
frugality  and  self-control  on  the  part  of  the  would-be  ancestors  of  the 
coming  Equilateral,  and  a  patient,  systematic,  and  continuous  development 
of  the  Isosceles  intellect  through  many  generations. 

1  "  What  need  of  a  certificate?"  a  Spaceland  critic  may  ask :  "  Is  not  the  procreation  of  a  Square 
Son  a  certificate  from  Nature  herself,  proving  the  Equal-sidedness  of  the  Father  ?  "  1  reply  that  no 
Lady  of  any  position  will  marry  an  uncertified  Triangle.  Square  offspring  has  sometimes  resulted 
from  a  slightly  Irregular  Triangle :  but  in  almost  every  such  case  the  Irregularity  of  the  first 
generation  is  visited  on  the  third  ;  which  either  fails  to  attain  the  Pentagonal  rank,  or  relapses  to 
the  Triangular. 

B 


io  Flat  land 

The  birth  of  a  True  Equilateral  Triangle  from  Isosceles  parents  is  the 
subject  of  rejoicing  in  our  country  for  many  furlongs  round.  After  a 
strict  eximination  conducted  by  the  Sanitary  and  Social  Board,  the  infant, 
if  certified  as  Regular,  is  with  solemn  ceremonial  admitted  into  the  class  of 
Equilaterals.  He  is  then  immediately  taken  from  his  proud  yet  sorrowing 
parents  and  adopted  by  some  childless  Equilateral,  who  is  bound  by  oath 
never  to  permit  the  child  henceforth  to  enter  his  former  home  or  so  much 
as  to  look  upon  his  relations  again,  for  fear  lest  the  freshly  developed 
organism  may,  by  force  of  unconscious  imitation,  fall  back  again  into  his 
hereditary  level. 

The  occasional  emergence  of  an  Isosceles  from  the  ranks  of  his  serf- 
born  ancestors,  is  welcomed  not  only  by  the  poor  serfs  themselves,  as  a 
gleam  of  light  and  hope  shed  upon  the  monotonous  squalor  of  their 
existence,  but  also  by  the  Aristocracy  at  large  ;  for  all  the  higher  classes 
are  well  aware  that  these  rare  phenomena,  while  they  do  little  or  nothing 
to  vulgarise  their  own  privileges,  serve  as  a  most  useful  barrier  against 
revolution  from  below. 

Had  the  acute-angled  rabble  been  all,  without  exception,  absolutely 
destitute  of  hope  and  of  ambition,  they  might  have  found  leaders  in  some 
of  their  many  seditious  outbreaks,  so  able  as  to  render  their  superior 
numbers  and  strength  too  much  even  for  the  wisdom  of  the  Circles. 
But  a  wise  ordinance  of  Nature  has  decreed  that,  in  proportion  as 
the  working-classes  increase  in  intelligence,  knowledge,  and  all  virtue, 
in  that  same  proportion  their  acute  angle  (which  makes  them  physically 
terrible)  shall  increase  also  and  approximate  to  the  harmless  angle  of 
the  Equilateral  Triangle.  Thus,  in  the  most  brutal  and  formidable  of 
the  soldier  class  creatures  almost  on  a  level  with  women  in  their  lack 
of  intelligence — it  is  found  that,  as  they  wax  in  the  mental  ability 
necessary  to  employ  their  tremendous  penetrating  power  to  advantage, 
so  do  they  wane  in  the  power  of  penetration  itself. 


1 1 

How  admirable  is  this  Law  of  Compensation !  And  how  perfect  a 
proof  of  the  natural  fitness  and,  I  may  almost  say,  the  divine  origin  of 
the  aristocratic  constitution  of  the  States  in  Flatland  !  By  a  judicious  use 
of  this  Law  of  Nature,  the  Polygons  and  Circles  are  almost  always  able 
to  stifle  sedition  in  its  very  cradle,  taking  advantage  of  the  irrepressible 
and  boundless  hopefulness  of  the  human  mind.'  Art  also  comes  to  the 
aid  of  Law  and  Order.  It  is  generally  found  possible — by  a  little  artificial 
compression  or  expansion  on  the  part  of  the  State  physicians — to  make 
some  of  the  more  intelligent  leaders  of  a  rebellion  perfectly  Regular,  and 
to  admit  them  at  once  into  the  privileged  classes  ;  a  much  larger  number, 
who  are  still  below  the  standard,  allured  by  the  prospect  of  being  ulti- 
mately ennobled,  are  induced  to  enter  the  State  Hospitals,  where  they  are 
kept  in  honourable  confinement  for  life ;  one  or  two  alone  of  the  more 
obstinate,  foolish,  and  hopelessly  irregular  are  led  to  execution. 

Then  the  wretched  rabble  of  the  Isosceles,  planless  and  leaderless,  are 
either  transfixed  without  resistance  by  the  small  body  of  their  brethren 
whom  the  Chief  Circle  keeps  in  pay  for  emergencies  of  this  kind ;  or  else 
more  often,  by  means  of  jealousies  and  suspicions  skilfully  fomented 
among  them  by  the  Circular  party,  they  are  stirred  to  mutual  warfare, 
and  perish  by  one  another's  angles.  No  less  than  one  hundred  and 
twenty  rebellions  are  recorded  in  our  annals,  besides  minor  outbreaks 
numbered  at  two  hundred  and  thirty-five  ;  and  they  have  all  ended  thus. 

§    4. — Concerning   the   Women. 

If  our  highly  pointed  Triangles  of  the  Soldier  class  are  formidable, 
it  may  be  readily  inferred  that  far  more  formidable  are  our  Women.  For, 
if  a  Soldier  is  a  wedge,  a  Woman  is  a  needle  ;  being,  so  to  speak,  all 
point,  at  least  at  the  two  extremities.  Add  to  this  the  power  of  making 
herself  practically  invisible  at  will,  and  you  will  perceive  that  a  Female, 

in  Flatland,  is  a  creature  by  no  means  to  be  trifled  with. 

B  2 


1 2  Flatland 

But  here,  perhaps,  some  of  my  younger  Readers  may  ask  how  a 
woman  in  Flatland  can  make  herself  invisible.  This  ought,  I  think,  to 
be  apparent  without  any  explanation.  However,  a  few  words  will  make 
it  clear  to  the  most  unreflecting. 

Place  a  needle  on  a  table.  Then,  with  your  eye  on  the  level  of  the 
table,  look  at  it  side-ways,  and  you  see  the  whole  length  of  it  ;  but  look 
at  it  end-ways,  and  you  see  nothing  but  a  point :  it  has  become  practically 
invisible.  Just  so  is  it  with  one  of  our  Women.  When  her  side  is  turned 
towards  us,  we  see  her  as  a  straight  line  ;  when  the  end  containing  her 
eye  or  mouth — for  with  us  these  two  organs  are  identical — is  the  part 
that  meets  our  eye,  then  we  see  nothing  but  a  highly  lustrous  point ;  but 
when  the  back  is  presented  to  our  view,  then — being  only  sub-lustrous, 
and,  indeed,  almost  as  dim  as  an  inanimate  object — her  hinder  extremity 
serves  her  as  a  kind  of  Invisible  Cap. 

The  dangers  to  which  we  are  exposed  from  our  Women  must  now 
be  manifest  to  the  meanest  capacity  in  Spaceland.  If  even  the  angle 
of  a  respectable  Triangle  in  the  middle  class  is  not  without  its  dangers ; 
if  to  run  against  a  Working  Man  involves  a  gash  ;  if  collision  with  an 
Officer  of  the  military  class  necessitates  a  serious  wound ;  if  a  mere  touch 
from  the  vertex  of  a  Private  Soldier  brings  with  it  danger  of  death  ; — 
what  can  it  be  to  run  against  a  Woman,  except  absolute  and  immediate 
destruction  ?  And  when  a  Woman  is  invisible,  or  visible  only  as  a  dim 
sub-lustrous  point,  how  difficult  must  it  be,  even  for  the  most  cautious, 
always  to  avoid  collision ! 

Many  are  the  enactments  made  at  different  times  in  the  different 
States  of  Flatland,  in  order  to  minimize  this  peril ;  and  in  the  Southern 
and  less  temperate  climates,  where  the  force  of  gravitation  is  greater, 
and  human  beings  more  liable  to  casual  and  involuntary  motions,  the 
Laws  concerning  Women  are  naturally  much  more  stringent.  But  a 
general  view  of  the  Code  may  be  obtained  from  the  following  summary  : — 


Flatland  1 3 

1.  Every  house  shall  have  one  entrance  in  the  Eastern  side,  for  the  use 
of  Females  only ;  by  which  all  females  shall  enter  "  in  a  becoming  and 
respectful  manner " *  and  not  by  the  Men's  or  Western  door. 

2.  No    Female    shall  walk   in   any  public  place  without    continually 
keeping  up  her  Peace-cry,  under  penalty  of  death. 

3.  Any  Female,  duly  certified  to  be  suffering  from  St.  Vitus's  Dance, 
fits,    chronic    cold    accompanied    by   violent    sneezing,    or    any    disease 
necessitating  involuntary  motions,  shall  be  instantly  destroyed. 

In  some  of  the  States  there  is  an  additional  Law  forbidding  Females, 
under  penalty  of  death,  from  walking  or  standing  in  any  public  place 
without  moving  their  backs  constantly  from  right  to  left  so  as  to  indicate 
their  presence  to  those  'behind  them ;  others  oblige  a  Woman,  when 
travelling,  to  be  followed  by  one  of  her  sons,  or  servants,  or  by  her 
husband  ;  others  confine  Women  altogether  to  their  houses  except  during 
the  religious  festivals.  But  it  has  been  found  by  the  wisest  of  our  Circles 
or  Statesmen  that  the  multiplication  of  restrictions  on  Females  tends 
not  only  to  the  debilitation  and  diminution  of  the  race,  but  also  to  the 
increase  of  domestic  murders  to  such  an  extent  that  a  State  loses 
more  than  it  gains  by  a  too  prohibitive  Code. 

For  whenever  the  temper  of  the  Women  is  thus  exasperated  by  con- 
finement at  home  or  hampering  regulations  abroad,  they  are  apt  to  vent 
their  spleen  upon  their  husbands  and  children  ;  and  in  the  less  temperate 
climates  the  whole  male  population  of  a  village  has  been  sometimes 
destroyed  in  one  or  two  hours  of  simultaneous  female  outbreak.  Hence 
the  Three  Laws,  mentioned  above,  suffice  for  the  better  regulated  States, 
and  may  be  accepted  as  a  rough  exemplification  of  our  Female  Code. 

After  all,  our  principal  safeguard  is  found,  not  in  Legislature,  but  in 

1  When  I  was  in  Spaceland  I  understood  that  some  of  your  Priestly  Circles  have  in  the  same 
way  a  separate  entrance  for  Villagers,  Fanners,  and  Teachers  of  Board  Schools  (Spectator,  Sept. 
1884,  p.  1255)  that  they  may  "approach  in  a  becoming  and  respectful  manner." 


14  Flat  land 

the  interests  of  the  Women  themselves.  For,  although  they  can  inflict 
instantaneous  death  by  a  retrograde  movement,  yet  unless  they  can  at 
once  disengage  their  stinging  extremity  from  the  struggling  body  of 
their  victim,  their  own  frail  bodies  are  liable  to  be  shattered. 

The  power  of  Fashion  is  also  on  our  side.  I  pointed  out  that  in  some 
less  civilised  States  no  female  is  suffered  to  stand  in  any  public  place  with- 
out swaying  her  back  from  right  to  left.  This  practice  has  been  universal 
among  ladies  of  any  pretensions  to  breeding  in  all  well-governed  States,  as 
far  back  as  the  memory  of  Figures  can  reach.  It  is  considered  a  disgrace 
to  any  State  that  legislation  should  have  to  enforce  what  ought  to  be,  and 
is  in  every  respectable  female,  a  natural  instinct.  The  rhythmical  and,  if  I 
may  so  say,  well-modulated  undulation  of  the  back  in  our  ladies  of  Circular 
rank  is  envied  and  imitated  by  the  wife  of  a  common  Equilateral,  who  can 
achieve  nothing  beyond  a  mere  monotonous  swing,  like  the  ticking  of  a 
pendulum  ;  and  the  regular  tick  of  the  Equilateral  is  no  less  admired  and 
copied  by  the  wife  of  the  progressive  and  aspiring  Isosceles,  in  the  females 
of  whose  family  no  "  back-motion  "  of  any  kind  has  become  as  yet  a 
necessity  of  life.  Hence,  in  every  family  of  position  and  consideration, 
"  back  motion  "  is  as  prevalent  as  time  itself ;  and  the  husbands  and  sons 
in  these  households  enjoy  immunity  at  least  from  invisible  attacks. 

Not  that  it  must  be  for  a  moment  supposed  that  our  Women  are 
destitute  of  affection.  But  unfortunately  the  passion  of  the  moment 
predominates,  in  the  Frail  Sex,  over  every  other  consideration.  This  is, 
of  course,  a  necessity  arising  from  their  unfortunate  conformation.  For 
as  they  have  no  pretensions  to  an  angle,  being  inferior  in  this  respect  to 
the  very  lowest  of  the,  Isosceles,  they  are  consequently  wholly  devoid  of 
brain-power,  and  have  neither  reflection,  judgment  nor  forethought,  and 
hardly  any  memory.  Hence,  in  their  fits  of  fury,  they  remember  no 
claims  and  recognise  no  distinctions.  I  have  actually  known  a  case 
where  a  Woman  has  exterminated  her  whole  household,  and  half  an  hour 


Flat  land  15 

afterwards,  when  her  rage  was  over  and  the  fragments  swept  away,  has 
asked  what  has  become  of  her  husband  and  her  children  ! 

Obviously  then  a  Woman  is  not  to  be  irritated  as  long  as  she  is  in  a 
position  where  she  can  turn  round.  When  you  have  them  in  thtir 
apartments — which  are  constructed  with  a  view  to  denying  them  that 
power — you  can  say  and  do  what  you  like ;  for  they  are  then  wholly 
impotent  for  mischief,  and  will  not  remember  a  few  minutes  hence  the 
incident  for  which  they  may  be  at  this  moment  threatening  you  with 
death,  nor  the  promises  which  you  may  have  found  it  necessary  to 
make  in  order  to  pacify  their  fury. 

On  the  whole  we  get  on  pretty  smoothly  in  our  domestic  relations, 
except  in  the  lower  strata  of  the  Military  Classes.  There  the  want  of  tact 
and  discretion  on  the  part  of  the  husbands  produces  at  times  indescribable 
disasters.  Relying  too  much  on  the  offensive  weapons  of  their  acute  angles 
instead  of  the  defensive  organs  of  good  sense  and  seasonable  simulations, 
these  reckless  creatures  too  often  neglect  the  prescribed  construction  of  the 
Women's  apartments,  or  irritate  their  wives  by  ill-advised  expressions 
out  of  doors,  which  they  refuse  immediately  to  retract.  Moreover  a  blunt 
and  stolid  regard  for  literal  truth  indisposes  them  to  make  those  lavish 
promises  by  which  the  more  judicious  Circle  can  in  a  moment  pacify  his 
consort.  The  result  is  massacre  ;  not  however  without  its  advantages, 
as  it  eliminates  the  more  brutal  and  troublesome  of  the  Isosceles  ;  and 
by  many  of  our  Circles  the  destructiveness  of  the  Thinner  Sex  is 
regarded  as  one  among  many  providential  arrangements  for  suppressing 
redundant  population,  and  nipping  Revolution  in  the  bud. 

Yet  even  in  our  best  regulated  and  most  approximately  circular  families 
I  cannot  say  that  the  ideal  of  family  life  is  so  high  as  with  you  in  Spaceland. 
There  is  peace,  in  so  far  as  the  absence  of  slaughter  may  be  called  by  that 
name,  but  there  is  necessarily  little  harmony  of  tastes  or  pursuits ;  and  the 
cautious  wisdom  of  the  Circles  has  ensured  safety  at  the  cost  of  domestic 


1 6  Flat  land 

comfort.  In  every  Circular  or  Polygonal  household  it  has  been  a  habit 
from  time  immemorial — and  has  now  become  a  kind  of  instinct  among 
the  women  of  our  higher  classes — that  the  mothers  and  daughters  should 
constantly  keep  their  eyes  and  mouths  towards  their  husband  and  his  male 
friends ;  and  for  a  lady  in  a  family  of  distinction  to  turn  her  back  upon  her 
husband  would  be  regarded  as  a  kind  of  portent,  involving  loss  of  status. 
But,  as  I  shall  soon  shew,  this  custom,  though  it  has  the  advantage  of 
safety,  is  not  without  its  disadvantages. 

In  the  house  of  the  Working  Man  or  respectable  Tradesman — where  the 
wife  is  allowed  to  turn  her  back  upon  her  husband,  while  pursuing  her 
household  avocations — there  are  at  least  intervals  of  quiet,  when  the  wife 
is  neither  seen  nor  heard,  except  for  the  humming  sound  of  the  continuous 
Peace-cry  ;  but  in  the  homes  of  the  upper  classes  there  is  too  often  no 
peace.  There  the  voluble  mouth  and  bright  penetrating  eye  are  ever 
directed  towards  the  Master  of  the  household  ;  and  light  itself  is  not 
more  persistent  than  the  stream  of  feminine  discourse.  The  tact  and 
skill  which  suffice  to  avert  a  Woman's  sting  are  unequal  to  the  task 
of  stopping  a  Woman's  mouth  ;  and  as  the  wife  has  absolutely  nothing 
to  say,  and  absolutely  no  constraint  of  wit,  sense,  or  conscience  to 
prevent  her  from  saying  it,  not  a  few  cynics  have  been  found  to  aver 
that  they  prefer  the  danger  of  the  death-dealing  but  inaudible  sting 
to  the  safe  sonorousness  of  a  Woman's  other  end. 

To  my  readers  in  Spaceland  the  condition  of  our  Women  may  seem 
truly  deplorable,  and  so  indeed  it  is.  A  Male  of  the  lowest  type  of  the 
Isosceles  may  look  forward  to  some  improvement  of  his  angle,  and  to  the 
ultimate  elevation  of  the  whole  of  his  degraded  caste  ;  but  no  Woman  can 
entertain  such  hopes  for  her  sex.  "  Once  a  Woman, always  a  Woman"  is  a 
Decree  of  Nature  ;  and  the  very  Laws  of  Evolution  seem  suspended  in  her 
disfavour.  Yet  at  least  we  can  admire  the  wise  Prearrangement  which  has 
ordained  that,  as  they  have  no  hopes,  so  they  shall  have  no  memory  to 


Flat  land  1 7 

recall,  and  no  forethought  to  anticipate,  the  miseries  and  humiliations 
which  are  at  once  a  necessity  of  their  existence  and  the  basis  of  the 
constitution  of  Flatland. 


§  5. — Of  our  methods   of  recognizing   one   another. 

You,  who  are  blessed  with  shade  as  well  as  light,  you  who  are  gifted 
with  two  eyes,  endowed  with  a  knowledge  of  perspective,  and  charmed 
with  the  enjoyment  of  various  colours,  you,  who  can  actually  see  an  angle, 
and  contemplate  the  complete  circumference  of  a  Circle  in  the  happy 
region  of  the  Three  Dimensions — how  shall  I  make  clear  to  you  the 
extreme  difficulty  which  we  in  Flatland  experience  in  recognizing  one 
another's  configurations  ? 

Recall  what  I  told  you  above.  All  beings  in  Flatland,  animate  or 
inanimate,  no  matter  what  their  form,  present  to  our  view  the  same,  or 
nearly  the  same,  appearance,  viz.  that  of  a  straight  Line.  How  then  can 
one  be  distinguished  from  another,  where  all  appear  the  same  ? 

The  answer  is  threefold.  The  first  means  of  recognition  is  the  sense  of 
hearing ;  which  with  us  is  far  more  highly  developed  than  with  you,  and 
which  enables  us  not  only  to  distinguish  by  the  voice  our  personal  friends, 
but  even  to  discriminate  between  different  classes,  at  least  so  far  as 
concerns  the  three  lowest  orders,  the  Equilateral,  the  Square,  and  the 
Pentagon — for  of  the  Isosceles  I  take  no  account.  But  as  we  ascend  in 
the  social  scale,  the  process  of  discriminating  and  being  discriminated 
by  hearing  increases  in  difficulty,  partly  because  voices  are  assimilated, 
partly  because  the  faculty  of  voice-discrimination  is  a  plebeian  virtue  not 
much  developed  among  the  Aristocracy.  And  wherever  there  is  any  danger 
of  imposture  we  cannot  trust  to  this  method.  Amongst  our  lowest  orders, 
the  vocal  organs  are  developed  to  a  degree  more  than  correspondent 
with  those  of  hearing,  so  that  an  Isosceles  can  easily  feign  the  voice  of  a 


i8  Flat  land 

Polygon,  and,  with   some  training,  that  of  a  Circle  himself.     A  second 
method  is  therefore  more  commonly  resorted  to. 

Feeling  is,  among  our  Women  and  lower  classes — about  our  upper 
classes  I  shall  speak  presently — the  principal  test  of  recognition,  at  all 
events  between  strangers,  and  when  the  question  is,  not  as  to  the  individual, 
but  as  to  the  class.  What  therefore  "  introduction"  is  among  the  higher 
classes  in  Spaceland,  that  the  process  of  "  feeling  "  is  with  us.  "  Permit  me 
to  ask  you  to  feel  and  be  felt  by  my  friend  Mr.  So-and-so  " — is  still,  among 
the  more  old-fashioned  of  our  country  gentlemen  in  districts  remote  from 
towns,  the  customary  formula  for  a  Flatland  introduction.  But  in  the 
towns,  and  among  men  of  business,  the  words  "  be  felt  by "  are  omitted 
and  the  sentence  is  abbreviated  to,  "  Let  me  ask  you  to  feel  Mr.  So-and- 
so  "  ;  although  it  is  assumed,  of  course,  that  the  "  feeling  "  is  to  be  recipro- 
cal. Among  our  still  more  modern  and  dashing  young  gentlemen — who 
are  extremely  averse  to  superfluous  effort  and  supremely  indifferent  to  the 
purity  of  their  native  language — the  formula  is  still  further  curtailed  by  the 
use  of  "to  feel"  in  a  technical  sense,  meaning,  "to  recommend-for-the 
purposes-of-feeling-and-being-felt "  ;  and  at  this  moment  the  "  slang  "  of 
polite  or  fast  society  in  the  upper  classes  sanctions  such  a  barbarism  as 
"  Mr.  Smith,  permit  me  to  feel  you  Mr.  Jones." 

Let  not  my  Reader  however  suppose  that  "  feeling "  is  with  us  the 
tedious  process  that  it  would  be  with  you.or  that  we  find  it  necessary  to  feel 
right  round  all  the  sides  of  every  individual  before  we  determine  the  class 
to  which  he  belongs.  Long  practice  and  training,  begun  in  the  schools  and 
continued  in  the  experience  of  daily  life,  enable  us  to  discriminate  at  once 
by  the  sense  of  touch,  between  the  angles  of  an  equal-sided  Triangle, 
Square,  and  Pentagon  ;  and  I  need  not  say  that  the  brainless  vertex  of  an 
acute-angled  Isosceles  is  obvious  to  the  dullest  touch.  It  is  therefore  not 
necessary,  as  a  rule,  to  do  more  than  feel  a  single  angle  of  any  individual ; 
and  this,  once  ascertained,  tells  us  the  class  of  the  person  whom  we  are 


Flat  land  19 

addressing,  unless  indeed  he  belongs  to  the  higher  sections  of  the  nobility. 
There  the  difficulty  is  much  greater.  Even  a  Master  of  Arts  in  our 
University  of  Wentbridge  has  been  known  to  confuse  a  ten-sided  with  a 
twelve-sided  Polygon  ;  and  there  is  hardly  a  Doctor  of  Science  in  or  out 
of  that  famous  University  who  could  pretend  to  decide  promptly  and 
unhesitatingly  between  a  twenty-sided  and  a  twenty-four  sided  member  of 
the  Aristocracy. 

Those  of  my  readers  who  recall  the  extracts  I  gave  above  from  the 
Legislative  code  concerning  Women,  will  readily  perceive  that  the  process 
of  introduction  by  contact  requires  some  care  and  discretion.  Otherwise 
the  angles  might  inflict  on  the  unwary  Feeler  irreparable  injury.  It 
is  essential  for  the  safety  of  the  Feeler  that  the  Felt  should  stand 
perfectly  still.  A  start,  a  fidgety  shifting  of  the  position,  yes,  even  a 
violent  sneeze,  has  been  known  before  now  to  prove  fatal  to  the  incau- 
tious, and  to  nip  in  the  bud  many  a  promising  friendship.  Especially 
is  this  true  among  the  lower  classes  of  the  Triangles.  With  them,  the 
eye  is  situated  so  far  from  their  vertex  that  they  can  scarcely  take 
cognizance  of  what  goes  on  at  that  extremity  of  their  frame.  They  are 
moreover  of  a  rough  coarse  nature,  not  sensitive  to  the  delicate  touch  of 
the  highly  organized  Polygon.  What  wonder  then  if  an  involuntary  toss 
of  the  head  has  ere  now  deprived  the  State  of  a  valuable  life ! 

I  have  heard  that  my  excellent  Grandfather — one  of  the  least  irregular 
of  his  unhappy  Isosceles  class,  who  indeed  obtained,  shortly  before 
his  decease,  four  out  of  seven  votes  from  the  Sanitary  and  Social  Board 
for  passing  him  into  the  class  of  the  Equal-sided — often  deplored  with 
a  tear  in  his  venerable  eye,  a  miscarriage  of  this  kind,  which  had  occurred 
to  his  great-great-great- Grand  father,  a  respectable  Working  Man  with 
an  angle  or  brain  of  59°  30'.  According  to  his  account,  my  unfortunate 
Ancestor,  being  afflicted  with  rheumatism,  and  in  the  act  of  being  felt 
by  a  Polygon,  by  one  sudden  start  accidentally  transfixed  the  Great  Man 


2O  Flatland 

through  the  diagonal ;  and  thereby,  partly  in  consequence  of  his  long 
imprisonment  and  degradation,  and  partly  because  of  the  moral  shock 
which  pervaded  the  whole  of  my  Ancestor's  relations,  threw  back  our 
family  a  degree  and  a  half  in  their  ascent  towards  better  things.  The 
result  was  that  in  the  next  generation  the  family  brain  was  registered 
at  only  58°,  and  not  till  the  lapse  of  five  generations  was  the  lost 
ground  recovered,  the  full  60°  attained,  and  the  Ascent  from  the  Isosceles 
finally  achieved.  And  all  this  series  of  calamities  from  one  little  accident 
in  the  process  of  Feeling. 

At  this  point  I  think  I  hear  some  of  my  better  educated  readers 
exclaim,  "  How  could  you  in  Flatland  know  anything  about  angles  and 
degrees,  or  minutes  ?  We  can  see  an  angle,  because  we  in  the  region  of 
Space,  can  see  two  straight  lines  inclined  to  one  another ;  but  you,  who 
can  see  nothing  but  one  straight  line  at  a  time,  or  at  all  events  only  a 
number  of  bits  of  straight  lines  all  in  one  straight  line, — how  can  you 
ever  discern  any  angle,  and  much  less  register  angles  of  different  sizes  ? " 

I  answer  that  though  we  cannot  see  angles,  we  can  infer  them,  and 
this  with  great  precision.  Our  sense  of  touch,  stimulated  by  necessity, 
and  developed  by  long  training,  enables  us  to  distinguish  angles  far  more 
accurately  than  your  sense  of  sight,  when  unaided  by  a  rule  or  measure 
of  angles.  Nor  must  I  omit  to  explain  that  we  have  great  natural  helps. 
It  is  with  us  a  Law  of  Nature  that  the  brain  of  the  Isosceles  class  shall 
begin  at  half  a  degree,  or  thirty  minutes,  and  shall  increase  (if  it  increases 
at  all)  by  half  a  degree  in  every  generation  ;  until  the  goal  of  60°  is 
reached,  when  the  condition  of  serfdom  is  quitted,  and  the  freeman  enters 
the  class  of  Regulars. 

Consequently,  Nature  herself  supplies  us  with  an  ascending  scale 
or  Alphabet  of  angles  for  half  a  degree  up  to  60°,  Specimens  of  which 
are  placed  in  every  Elementary  School  throughout  the  land.  Owing 
to  occasional  retrogressions,  to  still  more  frequent  moral  and  intellectual 


Flat  land  2 1 

stagnation,  and  to  the  extraordinary  fecundity  of  the  Criminal  and 
Vagabond  Classes,  there  is  always  a  vast  superfluity  of  individuals  of  the 
half  degree  and  single  degree  class,  and  a  fair  abundance  of  Specimens 
up  to  10°.  These  are  absolutely  destitute  of  civic  rights ;  and  a  great 
number  of  them,  not  having  even  intelligence  enough  for  the  purposes 
of  warfare,  are  devoted  by  the  States  to  the  service  of  education. 
Fettered  immovably  so  as  to  remove  all  possibility  of  danger,  they  are 
placed  in  the  class  rooms  of  our  Infant  Schools,  and  there  they  are 
utilized  by  the  Board  of  Education  for  the  purpose  of  imparting  to  the 
offspring  of  the  Middle  Classes  that  tact  and  intelligence  of  which  these 
wretched  creatures  themselves  are  utterly  devoid. 

In  some  states  the  Specimens  are  occasionally  fed  and  suffered  to 
exist  for  several  years ;  but  in  the  more  temperate  and  better  regulated 
regions,  it  is  found  in  the  long  run  more  advantageous  for  the  educational 
interests  of  the  young,  to  dispense  with  food,  and  to  renew  the  Specimens 
every  month, — which  is  about  the  average  duration  of  the  foodless 
existence  of  the  Criminal  class.  In  the  cheaper  schools,  what  is  gained 
by  the  longer  existence  of  the  Specimens  is  lost,  partly  in  the  expenditure 
for  food,  and  partly  in  the  diminished  accuracy  of  the  angles,  which 
are  impaired  after  a  few  weeks  of  constant  "  feeling."  Nor  must  we 
forget  to  add,  in  enumerating  the  advantages  of  the  more  expensive  system, 
that  it  tends,  though  slightly  yet  perceptibly,  to  the  diminution  of  the 
redundant  Isosceles  population — an  object  which  every  statesman  in 
Flatland  constantly  keeps  in  view.  On  the  whole  therefore — although 
I  am  not  ignorant  that,  in  many  popularly  elected  School  Boards,  there 
is  a  reaction  in  favour  of  "  the  cheap  system,"  as  it  is  called — I  am  myself 
disposed  to  think  that  this  is  one  of  the  many  cases  in  which  expense 
is  the  truest  economy. 

But  I  must  not  allow  questions  of  School  Board  politics  to  divert  me 
from  my  subject.  Enough  has  been  said,  I  trust,  to  show  that  Recognition 


22 


Flatland 


by  Feeling  is  not  so  tedious  or  indecisive  a  process  as  might  have  been 
supposed  ;  and  it  is  obviously  more  trustworthy  than  Recognition  by 
hearing.  Still  there  remain,  as  has  been  pointed  out  above,  the  objection 
that  this  method  is  not  without  danger. '  For  this  reason  many  in  the 
Middle  and  Lower  classes,  and  all  without  exception  in  the  Polygonal 
and  Circular  orders,  prefer  a  third  method,  the  description  of  which  shall 
be  reserved  for  the  next  section. 

§  6. — Of  Recognition  by  Sight. 

I  am  about  to  appear  very  inconsistent.  In  previous  sections  I  have 
said  that  all  figures  in  Flatland  present  the  appearance  of  a  straight  line  ; 
and  it  was  added  or  implied,  that  it  is  consequently  impossible  to  distin- 
guish by  the  visual  organ  between  individuals  of  different  classes  :  yet 
now  I  am  about  to  explain  to  my  Spaceland  Critics  how  we  are  able 
to  recognize  one  another  by  the  sense  of  sight. 

If  however  the  Reader  will  take  the  trouble  to  refer  to  the  passage 
in  which  Recognition  by  Feeling  is  stated  to  be  universal,  he  will  find 
this  qualification — "among  the  lower  classes."  It  is  only  among  the 
higher  classes  and  in  our  more  temperate  climates  that  Sight  Recognition 
is  practised. 

That  this  power  exists  in  any  regions  and  for  any  classes,  is  the  result 
of  Fog;  which  prevails  during  the  greater  part  of  the  year  in  all  parts 
save  the  torrid  zones.  That  which  is  with  you  in  Spaceland  an  unmixed 
evil,  blotting  out  the  landscape,  depressing  the  spirits,  and  enfeebling  the 
health,  is  by  us  recognized  as  a  blessing  scarcely  inferior  to  air  itself,  and 
as  the  Nurse  of  arts  and  Parent  of  sciences.  But  let  me  explain  my 
meaning,  without  further  eulogies  on  this  beneficent  Element. 

If  Fog  were  non-existent,  all  lines  would  appear  equally  and  in- 
distinguishably  clear ;  and  this  is  actually  the  case  in  those  unhappy 
countries  in  which  the  atmosphere  is  perfectly  dry  and  transparent. 


Flatland 


c 


D 


E 


But  wherever  there  is  a  rich  supply  of  Fog,  objects  that  are  at  a  distance, 
say  of  three  feet,  are  appreciably  dimmer  than  those  at  a  distance  of  two 
feet  eleven  inches  ;  and  the  result  is  that  by  careful  and  constant  experi- 
mental observation  of  comparative  dimness  and  clearness,  we  are  enabled 
to  infer  with  great  exactness  the  configuration  of  the  object  observed. 

An  instance  will  do  more  than  a  volume  of  generalities  to  make  my 
meaning  clear. 

Suppose  I  see  two  individuals  ap- 
proaching whose  rank  I  wish  to  ascertain. 
They  are,  we  will  suppose,  a  Merchant 
and  a  Physician,  or  in  other  words,  an 
Equilateral  Triangle  and  a  Pentagon  : 
how  am  I  to  distinguish  them  ? 

It  will  be  obvious,  to  every  child  in 
Spaceland  who  has  touched 
the  threshold  of  Geometrical 
Studies,  that,  if  I  can  bring 
my  eye  so  that  its  glance 
may  bisect  an  angle  (A)  of 
the  approaching  stranger, 
my  view  will  lie  as  it  were 
evenly  between  his  two 
sides  that  are  next  to  me 
(viz.  CA  and  AB),  so  that 

I  shall  contemplate  the  two  impartially,  and  both  will  appear  of  the 
same  size. 

Now  in  the  case  of  (i)  the  Merchant,  what  shall  I  see  ?  I  shall  see  a 
straight  line  DAE,  in  which  the  middle  point  (A)  will  be  very  bright  because 
it  is  nearest  to  me  ;  but  on  either  side  the  line  will  shade  away  rapidly  into 
dimness,  because  the  sides  AC  and  AD  recede  rapidly  into  the  fog ;  and 


24  Flat  land 

what  appear  to  me  as  the  Merchant's  extremities,  viz.  D  and  C,  will  be 
very  dim  indeed. 

On  the  other  hand  in  the  case  of  (2)  the  Physician,  though  I  shall  here 
also  see  a  line  (D'A'E)  with  a  bright  centre  (A7),  yet  it  will  shade  away  less 
rapidly  into  dimness,  because  the  sides  (A'C',  A'B7)  recede  less  rapidly  into 
the  fog ;  and  what  appear  to  me  the  Physician's  extremities,  viz.  D'  and  E', 
will  be  not  so  dim  as  the  extremities  of  the  Merchant. 

The  Reader  will  probably  understand  from  these  two  instances  how 
— after  a  very  long  training  supplemented  by  constant  experience — it  is 
possible  for  the  well-educated  classes  among  us  to  discriminate  with  fair 
accuracy  between  the  middle  and  lowest  orders,  by  the  sense  of  sight. 
If  my  Spaceland  Patrons  have  grasped  this  general  conception,  so  far  as 
to  conceive  the  possibility  of  it  and  not  to  reject  my  account  as  altogether 
incredible — I  shall  have  attained  all  I  can  reasonably  expect.  Were  I  to 
attempt  further  details  I  should  only  perplex.  Yet  for  the  sake  of  the 
young  and  inexperienced,  who  may  perchance  infer — from  the  two  simple 
instances  I  have  given  above,  of  the  manner  in  which  I  should  recognize 
my  Father  and  my  Sons — that  Recognition  by  sight  is  an  easy  affair,  it 
may  be  needful  to  point  out  that  in  actual  life  most  of  the  problems  of 
Sight  Recognition  are  far  more  subtle  and  complex. 

If  for  example,  when  my  Father,  the  Triangle,  approaches  me,  he 
happens  to  present  his  side  to  me  instead  of  his  angle,  then,  until  I  have 
asked  him  to  rotate,  or  until  I  have  edged  my  eye  round  him,  I  am  for 

the   moment   doubtful   whether 

"-•fit  he  may  not  be  a  Straight  Line, 

or,  in  other  words,  a  Woman. 
Again,  when  I  am  in  the  com- 
pany of  one  of  my  two  hexa- 
gonal Grandsons,  contemplating 
one  of  his  sides  (AB)  full  front, 


Flat  land  25 

it  will  be  evident  from  the  accompanying  diagram  that  I  shall  see 
one  whole  line  (AB)  in  comparative  brightness  (shading  off  hardly 
at  all  at  the  ends)  and  two  smaller  lines  (CA  and  BD)  dim  through- 
out and  shading  away  into  greater  dimness  toward  the  extremities 
C  and  D. 

But  I  must  not  give  way  to  the  temptation  of  enlarging  on  these 
topics.  The  meanest  mathematician  in  Spaceland  will  readily  believe  me 
when  I  assert  that  the  problems  of  life,  which  present  themselves  to  the 
well-educated — when  they  are  themselves  in  motion,  rotating,  advancing 
or  retreating,  and  at  the  same  time  attempting  to  discriminate  by  the 
sense  of  sight  between  a  number  of  Polygons  of  high  rank  moving  in 
different  directions,  as  for  example  in  a  ball-room  or  conversazione — 
must  be  of  a  nature  to  task  the  angularity  of  the  most  intellectual,  and 
amply  justify  the  rich  endowments  of  the  Learned  Professors  of  Geometry, 
both  Static  and  Kinetic,  in  the  illustrious  University  of  Wentbridge, 
where  the  Science  and  Art  of  Sight  Recognition  are  regularly  taught  to 
large  classes  of  the  elite  of  the  States. 

It  is  only  a  few  of  the  scions  of  our  noblest  and  wealthiest  houses, 
who  are  able  to  give  the  time  and  money  necessary  for  the  thorough 
prosecution  of  this  noble  and  valuable  Art.  Even  to  me,  a  Mathematician 
of  no  mean  standing,  and  the  Grandfather  of  two  most  hopeful  and 
perfectly  regular  Hexagons,  to  find  myself  in  the  midst  of  a  crowd  of 
rotating  Polygons  of  the  higher  classes,  is  occasionally  very  perplexing. 
And  of  course  to  a  common  Tradesman,  or  Serf,  such  a  sight  is  almost  as 
unintelligible  as  it  would  be  to  you,  my  Reader,  were  you  suddenly 
transported  into  our  country. 

In  such  a  crowd  you  could  see  on  all  sides  of  you  nothing  but  a  Line, 
apparently  straight,  but  of  which  the  parts  would  vary  irregularly  and 
perpetually  in  brightness  or  dimness.  Even  if  you  had  completed  your 
third  year  in  the  Pentagonal  and  Hexagonal  classes  in  the  University,  and 

C 


26  Flatland 

were  perfect  in  the  theory  of  the  subject,  you  would  still  find  that  there 
was  need  of  many  years  of  experience,  before  you  could  move  in  a 
fashionable  crowd  without  jostling  against  your  betters,  whom  it  is  against 
etiquette  to  ask  to  "  feel,"  and  who,  by  their  superior  culture  and  breeding, 
know  all  about  your  movements,  while  you  know  very  little  or  nothing 
about  theirs.  In  a  word,  to  comport  oneself  with  perfect  propriety  in 
Polygonal  society,  one  ought  to  be  a  Polygon  oneself.  Such  at  least  is 
the  painful  teaching  of  my  experience. 

It  is  astonishing  how  much  the  Art — or  I  may  almost  call  it  instinct — 
of  Sight  Recognition  is  developed  by  the  habitual  practice  of  it  and  by 
the  avoidance  of  the  custom  of  "  Feeling."  Just  as,  with  you,  the  deaf 
and  dumb,  if  once  allowed  to  gesticulate  and  to  use  the  hand-alphabet, 
will  never  acquire  the  more  difficult  but  far  more  valuable  art  of  lip-speech 
and  lip-reading,  so  it  is  with  us  as  regards  "  Seeing "  and  "  Feeling." 
None  who  in  early  life  resort  to  "Feeling"  will  ever  learn  "Seeing"  in 
perfection. 

For  this  reason,  among  our  Higher  Classes,  "  Feeling"  is  discouraged 
or  absolutely  forbidden.  From  the  cradle  their  children,  instead  of  going 
to  the  Public  Elementary  schools  (where  the  art  of  Feeling  is  taught,) 
are  sent  to  higher  Seminaries  of  an  exclusive  character ;  and  at  our  illus- 
trious University,  to  "  feel "  is  regarded  as  a  most  serious  fault,  involving 
Rustication  for  the  first  offence,  and  Expulsion  for  the  second. 

But  among  the  lower  classes  the  art  of  Sight  Recognition  is  regarded 
as  an  unattainable  luxury.  A  common  Tradesman  cannot  afford  to  let 
his  son  spend  a  third  of  his  life  in  abstract  studies.  The  children  of  the 
poor  are  therefore  allowed  to  "  feel "  from  their  earliest  years,  and  they 
gain  thereby  a  precocity  and  an  early  vivacity  which  contrast  at  first  most 
favourably  with  the  inert,  undeveloped,  and  listless  behaviour  of  the  half- 
instructed  youths  of  the  Polygonal  class  ;  but  when  the  latter  have  at  last 
completed  their  University  course,  and  are  prepared  to  put  their  theory 


Flatland  27 

into  practice,  the  change  that  comes  over  them  may  almost  be  described 
as  a  new  birth,  and  in  every  art,  science,  and  social  pursuit  they  rapidly 
overtake  and  distance  their  Triangular  competitors. 

Only  a  few  of  the  Polygonal  Class  fail  to  pass  the  Final  Test  or  Leav- 
ing Examination  at  the  University.  The  condition  of  the  unsuccessful 
minority  is  truly  pitiable.  Rejected  from  the  higher  class,  they  are  also 
despised  by  the  lower.  They  have  neither  the  matured  and  systematically 
trained  powers  of  the  Polygonal  Bachelors  and  Masters  of  Arts,  nor  yet 
the  native  precocity  and  mercurial  versatility  of  the  youthful  Tradesman. 
The  professions,  the  public  services  are  closed  against  them  ;  and  though 
in  most  States  they  are  not  actually  debarred  from  marriage,  yet  they 
have  the  greatest  difficulty  in  forming  suitable  alliances,  as  experience 
shows  that  the  offspring  of  such  unfortunate  and  ill-endowed  parents  is 
generally  itself  unfortunate,  if  not  positively  Irregular. 

It  is  from  these  specimens  of  the  refuse  of  our  Nobility  that  the  great 
Tumults  and  Seditions  of  past  ages  have  generally  derived  their  leaders ; 
and  so  great  is  the  mischief  thence  arising  that  an  increasing  minority  of 
our  more  progressive  Statesmen  are  of  opinion  that  true  mercy  would 
dictate  their  entire  suppression,  by  enacting  that  all  who  fail  to  pass  the 
Final  Examination  of  the  University  should  be  either  imprisoned  for  life, 
or  extinguished  by  a  painless  death. 

But  I  find  myself  digressing  into  the  subject  of  Irregularities,  a  matter 
of  such  vital  interest  that  it  demands  a  separate  section. 

§  7. — Of  Irregular  Figures. 

Throughout  the  previous  pages  I  have  been  assuming — what  perhaps 
should  have  been  laid  down  at  the  beginning  as  a  distinct  and  fundamental 
proposition — that  every  human  being  in  Flatland  is  a  Regular  Figure,  that 
is  to  say  of  regular  construction.  By  this  I  mean  that  a  Woman  must  not 
only  be  a  line,  but  a  straight  line  ;  that  an  Artisan  or  Soldier  must  have 

C  2 


28  Flatland 

two  of  his  sides  equal ;  that  Tradesmen  must  have  three  sides  equal ; 
Lawyers  (of  which  class  I  am  a  humble  member),  four  sides  equal,  and, 
generally,  that  in  every  Polygon,  all  the  sides  must  be  equal. 

The  size  of  the  sides  would  of  course  depend  upon  the  age  of  the 
individual.  A  Female  at  birth  would  be  about  an  inch  long,  while  a  tall 
adult  Woman  might  extend  to  a  foot.  As  to  the  Males  of  every  class, 
it  may  be  roughly  said  that  the  length  of  an  adult's  sides,  when  added 
together,  is  three  feet  or  a  little  more.  But  the  size  of  our  sides  is  not 
under  consideration.  I  am  speaking  of  the  equality  of  sides,  and  it 
does  not  need  "much  reflection  to  see  that  the  whole  of  the  social  life 
in  Flatland  rests  upon  the  fundamental  fact  that  Nature  wills  all  Figures 
to  have  their  sides  equal. 

If  our  sides  were  unequal  our  angles  would  be  unequal.  Instead  of 
its  being  sufficient  to  feel,  or  estimate  by  sight,  a  single  angle  in  order  to 
determine  the  form  of  an  individual,  it  would  be  necessary  to  ascertain 
each  angle  by  the  experiment  of  Feeling.  But  life  would  be  too  short  for 
such  a  tedious  groping.  The  whole  science  and  art  of  Sight  Recognition 
would  at  once  perish  ;  Feeling,  so  far  as  it  is  an  art,  would  not  long  survive  ; 
intercourse  would  become  perilous  or  impossible  ;  there  would  be  an  end 
to  all  confidence,  all  forethought ;  no  one  would  be  safe  in  making  the 
most  simple  social  arrangements;  in  a  word,  civilization  would  relapse 
into  barbarism. 

Am  I  going  too  fast  to  carry  my  Readers  with  me  to  these  obvious 
conclusions  ?  Surely  a  moment's  reflection,  and  a  single  instance  from 
common  life,  must  convince  every  one  that  our  whole  social  system  is 
based  upon  Regularity,  or  Equality  of  Angles.  You  meet,  for  example, 
two  or  three  Tradesmen  in  the  street,  whom  you  recognize  at  once  to  be 
Tradesmen  by  a  glance  at  their  angles  and  rapidly  bedimmed  sides,  and 
you  ask  them  to  step  into  your  house  to  lunch.  This  you  do  at  present 
with  perfect  confidence,  because  every  one  knows  to  an  inch  or  two  the 


Flatland  29 

area  occupied  by  an  adult  Triangle  :  but  imagine  that  your  Tradesman 
drags  behind  his  regular  and  respectable  vertex,  a  parallelogram  of  twelve 
or  thirteen  inches  in  diagonal : — what  are  you  to  do  with  such  a  monster 
sticking  fast  in  your  house  door  ? 

But  I  am  insulting  the  intelligence  of  my  Readers  by  accumulating 
details  which  must  be  patent  to  every  one  who  enjoys  the  advantages  of 
a  Residence  in  Spaceland.  Obviously  the  measurements  of  a  single  angle 
would  no  longer  be  sufficient  under  such  portentous  circumstances;  one's 
whole  life  would  be  taken  up  in  feeling  or  surveying  the  perimeter  of  one's 
acquaintances.  Already  the  difficulties  of  avoiding  a  collision  in  a  crowd 
are  enough  to  tax  the  sagacity  of  even  a  well-educated  Square ;  but  if  no 
one  could  calculate  the  Regularity  of  a  single  figure  in  the  company,  all 
would  be  chaos  and  confusion,  and  the  slightest  panic  would  cause  serious 
injuries,  or — if  there  happened  to  be  any  Women  or  Soldiers  present — 
perhaps  considerable  loss  of  life. 

Expediency  therefore  concurs  with  Nature  in  stamping  the  seal  of  its 
approval  upon  Regularity  of  conformation  :  nor  has  the  Law  been  backward 
in  seconding  their  efforts.  "  Irregularity  of  Figure "  means  with  us  the 
same  as,  or  more  than,  a  combination  of  moral  obliquity  and  criminality 
with  you,  and  is  treated  accordingly.  There  are  not  wanting,  it  is  true, 
some  promulgators  of  paradoxes  who  maintain  that  there  is  no  necessary 
connection  between  geometrical  and  moral  Irregularity.  "The  Irregular," 
they  say,  "is  from  his  birth  scouted  by  his  own  parents,  derided  by  his 
brothers  and  sisters,  neglected  by  the  domestics,  scorned  and  suspected  by 
society,  and  excluded  from  all  posts  of  responsibility,  trust,  and  useful 
activity.  His  every  movement  is  jealously  watched  by  the  police  till  he 
comes  of  age  and  presents  himself  for  inspection  ;  then  he  is  either  destroyed, 
if  he  is  found  to  exceed  the  fixed  margin  of  deviation,  or  else  immured 
in  a  Government  Office  as  a  clerk  of  the  seventh  class ;  prevented  from 
marriage ;  forced  to  drudge  at  an  uninteresting  occupation  for  a  miserable 


30  Flatland 

stipend  ;  obliged  to  live  and  board  at  the  office,  and  to  take  even  his 
vacation  under  close  supervision ;  what  wonder  that  human  nature,  even 
in  the  best  and  purest,  is  embittered  and  perverted  by  such  surroundings  ! " 

All  this  very  plausible  reasoning  does  not  convince  me,  as  it  has  not 
convinced  the  wisest  of  our  Statesmen,  that  our  ancestors  erred  in  laying 
it  down  as  an  axiom  of  policy  that  the  toleration  of  Irregularity  is 
incompatible  with  the  safety  of  the  State.  Doubtless,  the  life  of  an 
Irregular  is  hard  ;  but  the  interests  of  the  Greater  Number  require  that 
it  shall  be  hard.  If  a  man  with  a  triangular  front  and  a  polygonal  back 
were  allowed  to  exist  and  to  propagate  a  still  more  Irregular  posterity, 
what  would  become  of  the  arts  of  life  ?  Are  the  houses  and  doors  and 
churches  in  Flatland  to  be  altered  in  order  to  accommodate  such  monsters  ? 
Are  our  ticket-collectors  to  be  required  to  measure  every  man's  perimeter 
before  they  allow  him  to  enter  a  theatre,  or  to  take  his  place  in  a  lecture 
room  ?  Is  an  Irregular  to  be  exempted  from  the  militia  ?  And  if  not,  how 
is  he  to  be  prevented  from  carrying  desolation  into  the  ranks  of  his 
comrades  ?  Again,  what  irresistible  temptations  to  fraudulent  impostures 
must  needs  beset  such  a  creature !  How  easy  for  him  to  enter  a  shop  with 
his  polygonal  front  foremost,  and  to  order  goods  to  any  extent  from  a 
confiding  tradesman  !  Let  the  advocates  of  a  falsely  called  Philanthropy 
plead  as  they  may  for  the  abrogation  of  the  Irregular  Penal  Laws,  I  for 
my  part  have  never  known  an  Irregular  who  was  not  also  what  Nature 
evidently  intended  him  to  be — a  hypocrite,  a  misanthropist,  and,  up  to 
the  limits  of  his  power — a  perpetrator  of  all  manner  of  mischief. 

Not  that  I  should  be  disposed  to  recommend  (at  present)  the  extreme 
measures  adopted  in  some  States,  where  an  infant  whose  angle  deviates 
by  half  a  degree  from  the  correct  angularity  is  summarily  destroyed  at 
birth.  Some  of  our  highest  and  ablest  men,  men  of  real  genius,  have 
during  their  earliest  days  laboured  under  deviations  as  great  as,  or  even 
greater  than,  forty-five  minutes  :  and  the  loss  of  their  precious  lives 


Flatland  3 1 

< 

would  have  been  an  irreparable  injury  to  the  State.  The  art  of  healing 
also  has  achieved  some  of  its  most  glorious  triumphs  in  the  compressions, 
extensions,  trepannings,  colligations,  -and  other  surgical  or  diaetetic 
operations  by  which  Irregularity  has  been  partly  or  wholly  cured.  Ad- 
vocating therefore  a  Via  Media,  I  would  lay  down  no  fixed  or  absolute 
line  of  demarcation ;  but  at  the  period  when  the  frame  is  just  beginning 
to  set,  and  when  the  Medical  Board  has  reported  that  recovery  is  im- 
probable, I  would  suggest  that  the  Irregular  offspring  be  painlessly  and 
mercifully  consumed. 

§  8. — Of  the  Ancient  Practice  of  Painting. 

If  my  Readers  have  followed  me  with  any  attention  up  to  this  point, 
they  will  not  be  surprised  to  hear  that  life  is  somewhat  dull  in  Flatland.  I 
do  not,  of  course,  mean  that  there  are  not  battles,  conspiracies,  tumults, 
factions,  and  all  those  other  phenomena  which  are  supposed  to  make 
History  interesting ;  nor  would  I  deny  that  the  strange  mixture  of  the 
problems  of  life  and  the  problems  of  Mathematics,  continually  inducing 
conjecture  and  giving  the  opportunity  of  immediate  verification,  imparts 
to  our  existence  a  zest  which  you  in  Spaceland  can  hardly  comprehend.  I 
speak  now  from  the  aesthetic  and  artistic  point  of  view  when  I  say  that 
life  with  us  is  dull ;  aesthetically  and  artistically,  very  dull  indeed. 

How  can  it  be  otherwise,  when  all  one's  prospect,  all  one's  landscapes, 
historical  pieces,  portraits,  flowers,  still  life,  are  nothing  but  a  single  line, 
with  no  varieties  except  degrees  of  brightness  and  obscurity  ? 

It  was  not  always  thus.  Colour,  if  Tradition  speaks  the  truth,  once  for 
the  space  of  half  a  dozen  centuries  or  more,  threw  a  transient  charm  upon 
the  lives  of  our  ancestors  in  the  remotest  ages.  Some  private  individual 
— a  Pentagon  whose  name  is  variously  reported — having  casually  dis- 
covered the  constituents  of  the  simpler  colours  and  a  rudimentary  method  of 
painting,  is  said  to  have  begun  by  decorating  first  his  house,  then  his  slaves, 


32  Flat  I  and 

then  his  Father,  his  Sons  and  Grandsons,  lastly  himself.  The  convenience 
as  well  as  the  beauty  of  the  results  commended  themselves  to  all. 
Wherever  Chromatistes, — for  by  that  name  the  most  trustworthy  authorities 
concur  in  calling  him, — turned  his  variegated  frame,  there  he  at  once 
excited  attention,  and  attracted  respect.  No  one  now  needed  to  "  feel " 
him  ;  no  one  mistook  his  front  for  his  back ;  all  his  movements  were 
readily  ascertained  by  his  neighbours  without  the  slightest  strain  on 
their  powers  of  calculation;  no  one  jostled  him,  or  failed  to  make  way  for 
him ;  his  voice  was  saved  the  labour  of  that  exhausting  utterance  by 
which  we  colourless  Squares  and  Pentagons  are  often  forced  to  proclaim 
our  individuality  when  we  move  amid  a  crowd  of  ignorant  Isosceles. 

The  fashion  spread  like  wildfire.  Before  a  week  was  over,  every  Square 
and  Triangle  in  the  district  had  copied  the  example  of  Chromatistes,  and 
only  a  few  of  the  more  conservative  Pentagons  still  held  out.  A  month  or 
two  found  even  the  Dodecagons  infected  with  the  innovation.  A  year 
had  not  elapsed  before  the  habit  had  spread  to  all  but  the  very  highest 
of  the  Nobility.  Needless  to  say,  the  custom  soon  made  its  way  from  the 
district  of  Chromatistes  to  surrounding  regions  ;  and  within  two  generations 
no  one  in  all  Flatland  was  colourless  except  the  Women  and  the  Priests. 

Here  Nature  herself  appeared  to  erect  a  barrier,  and  to  plead  against 
extending  the  innovation  to  these  two  classes.  Many-sidedness  was  almost 
essential  as  a  pretext  for  the  Innovators.  "  Distinction  of  sides  is  intended 
by  Nature  to  imply  distinction  of  colours  " — such  was  the.  sophism  which 
in  those  days  flew  from  mouth  to  mouth,  converting  whole  towns  at  a  time 
to  the  new  culture.  But  manifestly  to  our  Priests  and  Women  this  adage 
did  not  apply.  The  latter  had  only  one  side,  and  therefore — plurally  and 
pedantically  speaking — no  sides.  The  former — if  at  least  they  would 
assert  their  claim  to  be  really  and  truly  Circles,  and  not  mere  high-class 
Polygons  with  an  infinitely  large  number  of  infinitesimally  small  sides — 
were  in  the  habit  of  boasting  (what  Women  confessed  and  deplored)  that 


Flatland  33 

they  also  had  no  sides,  being  blessed  with  a  perimeter  of  one  line  or,  in 
other  words,  a  Circumference.  Hence  it  came  to  pass  that  these  two 
Classes  could  see  no  force  in  the  so-called  axiom  about  "  Distinction  of 
Sides  implying  Distinction  of  Colour"  ;  and  when  all  others  had  succumbed 
to  the  fascinations  of  corporal  decoration,  the  Priests  and  the  Women  alone 
still  remained  pure  from  the  pollution  of  paint. 

Immoral,  licentious,  anarchical,  unscientific — call  them  by  what  names 
you  will — yet,  from  an  aesthetic  point  of  view,  those  ancient  days  of  the 
Colour  Revolt  were  the  glorious  childhood  of  Art  in  Flatland — a  childhood, 
alas,  that  never  ripened  into  manhood,  nor  even  reached  the  blossom  of 
youth.  To  live  was  then  in  itself  a  delight,  because  living  implied  seeing. 
Even  at  a  small  party,  the  company  was  a  pleasure  to  behold  ;  the  richly 
varied  hues  of  the  assembly  in  a  church  or  theatre  are  said  to  have  more 
than  once  proved  too  distracting  for  our  greatest  teachers  and  actors  ;  but 
most  ravishing  of  all  is  said  to  have  been  the  unspeakable  magnificence  of 
a  military  review. 

The  sight  of  a  line  of  battle  of  twenty  thousand  Isosceles  suddenly 
facing  about,  and  exchanging  the  sombre  black  of  their  bases  for  the  orange 
and  purple  of  the  two  sides  including  their  acute  angle  ;  the  militia  of  the 
Equilateral  Triangles  tricoloured  in  red,  white,  and  blue  ;  the  mauve,  ultra- 
marine, gamboge,  and  burnt  umber  of  the  Square  artillerymen  rapidly 
rotating  near  their  vermilion  guns ;  the  dashing  and  flashing  of  the  five- 
coloured  and  six-coloured  Pentagons  and  Hexagons  careering  across  the 
field  in  their  offices  of  surgeons,  geometricians  and  aides-de-camp — 
all  these  may  well  have  been  sufficient  to  render  credible  the  famous 
story  how  an  illustrious  Circle,  overcome  by  the  artistic  beauty  of  the  forces 
under  his  command,  threw  aside  his  marshal's  baton  and  his  royal  crown, 
exclaiming  that  he  henceforth  exchanged  them  for  the  artist's  pencil.  How 
great  and  glorious  the  sensuous  development  of  these  days  must  have  been 
is  in  part  indicated  by  the  very  language  and  vocabulary  of  the  period. 


34  Flatland 

The  commonest  utterances  of  the  commonest  citizens  in  the  time  of  the 
Colour  Revolt  seem  to  have  been  suffused  with  a  richer  tinge  of  word  or 
thought ;  and  to  that  era  we  are  even  now  indebted  for  our  finest  poetry 
and  for  whatever  rhythm  still  remains  in  the  more  scientific  utterance  of 
these  modern  days. 

§  9. — Of  the  Universal  Colour  Bill. 

But  meanwhile  the  intellectual  Arts  were  fast  decaying. 

The  Art  of  Sight  Recognition,  being  no  longer  needed,  was  no  longer 
practised  ;  and  the  studies  of  Geometry,  Statics,  Kinetics,  and  other  kindred 
subjects,  came  soon  to  be  considered  superfluous,  and  fell  into  disrepute 
and  neglect  even  at  our  University.  The  inferior  Art  of  Feeling  speedily 
experienced  the  same  fate  at  our  Elementary  Schools.  Then  the  Isosceles 
classes,  asserting  that  the  Specimens  were  no  longer  used  nor  needed,  and 
refusing  to  pay  the  customary  tribute  from  the  Criminal  classes  to  the 
service  of  Education,  waxed  daily  more  numerous  and  more  insolent 
on  the  strength  of  their  immunity  from  the  old  burden  which  had  formerly 
exercised  the  twofold  wholesome  effect  of  at  once  taming  their  brutal 
nature  and  thinning  their  excessive  numbers. 

Year  by  year  the  Soldiers  and  Artisans  began  more  vehemently  to 
assert — and  with  increasing  truth — that  there  was  no  great  difference 
between  them  and  the  very  highest  class  of  Polygons,  now  that  they  were 
raised  to  an  equality  with  the  latter,  and  enabled  to  grapple  with  all  the 
difficulties  and  solve  all  the  problems  of  life,  whether  Statical  and  Kinetical, 
by  the  simple  process  of  Colour  Recognition.  Not  content  with  the  natural 
neglect  into  which  Sight  Recognition  was  falling,  they  began  boldly  to 
demand  the  legal  prohibition  of  all  "  monopolising  and  aristocratic  Arts  " 
and  the  consequent  abolition  of  all  endowments  for  the  studies  of  Sight 
Recognition,  Mathematics,  and  Feeling.  Soon,  they  began  to  insist  that 
inasmuch  as  Colour,  which  was  a  second  Nature,  had  destroyed  the  need 


Flatland  35 

of  aristocratic  distinctions,  the  Law  should  follow  in  the  same  path,  and 
that  henceforth  all  individuals  and  all  classes  should  be  recognized  as 
absolutely  equal  and  entitled  to  equal  rights. 

Finding  the  higher  Orders  wavering  and  undecided,  the  leaders  of  the 
Revolution  advanced  still  further  in  their  requirements,  and  at  last 
demanded  that  all  classes  alike,  the  Priests  and  the  Women  not  excepted, 
should  do  homage  to  Colour  by  submitting  to  be  painted.  When  it  was 
objected  that  Priests  and  Women  had  no  sides,  they  retorted  that  Nature 
and  Expediency  concurred  in  dictating  that  the  front  half  of  every  human 
being  (that  is  to  say,  the  half  containing  his  eye  and  mouth)  should  be 
distinguishable  from  his  hinder  half.  They  therefore  brought  before  a 
general  and  extraordinary  Assembly  of  all  the  States  of  Flatland  a  Bill 
proposing  that  in  every  Woman  the  half  containing  the  eye  and  mouth 
should  be  coloured  red,  and  the  other  half  green.  The  Priests  were  to  be 
painted  in  the  same  way,  red  being  applied  to  that  semicircle  in  which  the 
eye  and  mouth  formed  the  middle  point ;  while  the  other  or  hinder  semi- 
circle was  to  be  coloured  green. 

There  was  no  little  cunning  in  this  proposal,  which  indeed  emanated, 
not  from  any  Isosceles  —for  no  being  so  degraded  would  have  had 
angularity  enough  to  appreciate,  much  less  to  devise,  such  a  model  of 
state-craft — but  from  an  Irregular  Circle  who,  instead  of  being  destroyed 
in  his  childhood,  was  reserved  by  a  foolish  indulgence  to  bring  desolation 
on  his  country  and  destruction  on  myriads  of  his  followers. 

On  the  one  hand  the  proposition  was  calculated  to  bring  the  Women 
in  all  classes  over  to  the  side  of  the  Chromatic  Innovation.  For  by 
assigning  to  the  Women  the  same  two  colours  as  were  assigned  to  the 
Priests,  the  Revolutionists  thereby  ensured  that,  in  certain  positions,  every 
Woman  would  appear  like  a  Priest,  and  be  treated  with  corresponding 
respect  and  deference — a  prospect  that  could  not  fail  to  attract  the  Female 
Sex  in  a  mass. 


36  Flatland 

But  by  some  of  my  Readers  the  possibility  of  the  identical  appearance 
of  Priests  and  Women,  under  the  new  Legislation,  may  not  be  recognized  ; 
if  so,  a  word  or  two  will  make  it  obvious. 

Imagine  a  woman  duly  decorated,  according  to  the  new  Code ;  with 
the  front  half  (i.e.  the  half  containing  eye  and  mouth)  red,  and  with  the 
hinder  half  green.  Look  at  her  from  one  side.  Obviously  you  will  see 
a  straight  line,  half  red,  half  green. 

Now  imagine  a  Priest,  whose 
mouth  is  at  M,  and  whose  front 
semicircle  (AMB)  is  consequently 
coloured  red,  while  his  hinder 
semicircle  is  green  ;  so  that  the 
diameter  AB  divides  the  green 
from  the  red.  If  you  contemplate 
the  Great  Man  so  as  to  have 
your  eye  in  the  same  straight 

line  as  his  dividing  diameter  (AB),  what  you  will  see  will  be  a  straight  line 
(CBD),  of  which  one  half  (CB)  will  be  red,  and  the  other  (BD)  green.  The 
whole  line  (CD)  will  be  rather  shorter  perhaps  than  that  of  a  full-sized 
Woman,  and  will  shade  off  more  rapidly  towards  its  extremities ;  but  the 
identity  of  the  colours  would  give  you  an  immediate  impression  of  identity 
if  not  Class,  making  you  neglectful  of  other  details.  Bear  in  mind  the 
decay  of  Sight  Recognition  which  threatened  society  at  the  time  of  the 
Colour  Revolt ;  add  too  the  certainty  that  Women  would  speedily  learn 
to  shade  off  their  extremities  so  as  to  imitate  the  Circles ;  it  must  then 
be  surely  obvious  to  you,  my  dear  Reader,  that  the  Colour  Bill  placed  us 
under  a  great  danger  of  confounding  a  Priest  with  a  young  Woman. 

How  attractive  this  prospect  must  have  been  to  the  Frail  Sex  may 
readily  be  imagined.  They  anticipated  with  delight  the  confusion  that 
would  ensue.  At  home  they  might  hear  political  and  ecclesiastical  secrets 


Flatland  37 

intended  not  for  them  but  for  their  husbands  and  brothers,  and  might  even 
issue  commands  in  the  name  of  a  priestly  Circle  ;  out  of  doors  the  striking 
combination  of  red  and  green,  without  addition  of  any  other  colours,  would 
be  sure  to  lead  the  common  people  into  endless  mistakes,  and  the  Women 
would  gain  whatever  the  Circles  lost,  in  the  deference  of  the  passers  by. 
As  for  the  scandal  that  would  befall  the  Circular  Class  if  the  frivolous  and 
unseemly  conduct  of  the  Women  were  imputed  to  them,  and  as  to  the 
consequent  subversion  of  the  Constitution,  the  Female  Sex  could  not  be 
expected  to  give  a  thought  to  these  considerations.  Even  in  the  house- 
holds of  the  Circles,  the  Women  were  all  in  favour  of  the  Universal 
Colour  Bill. 

The  second "  object  aimed  at  by  the  Bill  was  the  gradual  demor- 
alization of  the  Circles  themselves.  In  the  general  intellectual  decay  they 
still  preserved  their  pristine  clearness  and  strength  of  understanding. 
From  their  earliest  childhood,  familiarized  in  their  Circular  households 
with  the  total  absence  of  Colour,  the  Nobles  alone  preserved  the  Sacred 
Art  of  Sight  Recognition,  with  all  the  advantages  that  result  from  that 
admirable  training  of  the  intellect.  Hence,  up  to  the  date  of  the  intro- 
duction of  the  Universal  Colour  Bill,  the  Circles  had  not  only  held  their 
own,  but  even  increased  their  lead  of  other  classes  by  abstinence  from 
the  popular  fashion. 

Now  therefore  the  artful  Irregular  whom  I  described  above  as  the  real 
author  of  this  diabolical  Bill,  determined  at  one  blow  to  lower  the  status  of 
the  Hierarchy  by  forcing  them  to  submit  to  the  pollution  of  Colour,  and  at 
the  same  time  to  destroy  their  domestic  opportunities  of  training  in  the 
Art  of  Sight  Recognition,  so  as  to  enfeeble  their  intellects  by  depriving 
them  of  their  pure  and  colourless  homes.  Once  subjected  to  the  chromatic 
taint,  every  parental  and  every  childish  Circle  would  demoralize  each  other. 
Only  in  discerning  between  the  Father  and  the  Mother  would  the  Circular 
infant  find  problems  for  the  exercise  of  its  understanding — problems  too 


38  Flatland 

often  likely  to  be  corrupted  by  maternal  impostures  with  the  result  of 
shaking  the  child's  faith  in  all  logical  conclusions.  Thus  by  degrees  the 
intellectual  lustre  of  the  Priestly  Order  would  wane,  and  the  road  would 
then  lie  open  for  a  total  destruction  of  all  Aristocratic  Legislature  and  for 
the  subversion  of  our  Privileged  Classes. 

§  10. — Of  the  Suppression  of  the  Chromatic  Sedition. 

The  agitation  for  the  Universal  Colour  Bill  continued  for  three  years  ; 
and  up  to  the  last  moment  of  that  period  it  seemed  as  though  Anarchy 
were  destined  to  triumph. 

A  whole  army  of  Polygons,  who  turned  out  to  fight  as  private  soldiers, 
was  utterly  annihilated  by  a  superior  force  of  Isosceles  Triangles — the 
Squares  and  Pentagons  meanwhile  remaining  neutral.  Worse  than  all,  some 
of  the  ablest  Circles  fell  a  prey  to  conjugal  fury.  Infuriated  by  political 
animosity,  the  wives  in  many  a  noble  household  wearied  their  lords  with 
prayers  to  give  up  their  opposition  to  the  Colour  Bill ;  and  some,  rinding 
their  entreaties  fruitless,  fell  on  and  slaughtered  their  innocent  children  and 
husbands,  perishing  themselves  in  the  act  of  carnage.  It  is  recorded  that 
during  that  triennial  agitation  no  less  than  twenty-three  Circles  perished  in 
domestic  discord. 

Great  indeed  was  the  peril.  It  seemed  as  though  the  Priests  had  no 
choice  between  submission  and  extermination  ;  when  suddenly  the  course 
of  events  was  completely  changed  by  one  of  those  picturesque  incidents 
which  Statesmen  ought  never  to  neglect,  often  to  anticipate,  and  some- 
times perhaps  to  originate,  because  of  the  absurdly  disproportionate  power 
with  which  they  appeal  to  the  sympathies  of  the  populace. 

It  happened  that  an  Isosceles  of  a  low  type,  with  a  brain  little  if 
at  all  above  four  degrees — accidentally  dabbling  in  the  colours  of  some 
Tradesman  whose  shop  he  had  plundered — painted  himself,  or  caused 
himself  to  be  painted  (for  the  story  varies)  with  the  twelve  colours  of  a 


Flatland  39 

Dodecahedron.  Going  into  the  Market  Place  he  accosted  in  a  feigned 
voice  a  maiden,  the  orphan  daughter  of  a  noble  Polygon,  whose  affection  in 
former  days  he  had  sought  in  vain ;  and  by  a  series  of  deceptions,  aided  on 
the  one  side  by  a  string  of  lucky  accidents  too  long  to  relate,  and,  on  the 
other,  by  an  almost  inconceivable  fatuity  and  neglect  of  ordinary  pre- 
cautions on  the  part  of  the  relations  of  the  bride,  he  succeeded  in  con- 
summating the  marriage.  The  unhappy  girl  committed  suicide  on 
discovering  the  fraud  to  which  she  had  been  subjected. 

When  the  news  of  this  catastrophe  spread  from  State  to  State  the 
minds  of  the  Women  were  violently  agitated.  Sympathy  with  the 
miserable  victim  and  anticipations  of  similar  deceptions  for  themselves, 
their  sisters,  and  their  daughters,  made  them  now  regard  the  Colour  Bill  in 
an  entirely  new  aspect.  Not  a  few  openly  avowed  themselves  converted  to 
antagonism ;  the  rest  needed  only  a  slight  stimulus  to  make  a  similar 
avowal.  Seizing  this  favourable  opportunity  the  Circles  hastily  convened 
an  extraordinary  Assembly  of  the  States ;  and  besides  the  usual  guard  of 
Convicts,  they  secured  the  attendance  of  a  large  number  of  reactionary 
Women. 

Amidst  an  unprecedented  concourse,  the  Chief  Circle  of  those  days — by 
name  Pantocyclus — arose  to  find  himself  hissed  and  hooted  by  a  hundred 
and  twenty  thousand  Isosceles.  But  he  secured  silence  by  declaring  that 
henceforth  the  Circles  would  enter  on  a  policy  of  Concession  ;  yielding  to 
the  wishes  of  the  majority,  they  would  accept  the  Colour  Bill.  The 
uproar  being  at  once  converted  to  applause,  he  invited  Chromatistes,  the 
leader  of  the  Sedition,  into  the  centre  of  the  hall,  to  receive  in  the  name  of 
his  followers  the  submission  of  the  Hierarchy.  Then  followed  a  speech,  a 
masterpiece  of  rhetoric,  which  occupied  nearly  a  day  in  the  delivery,  and 
to  which  no  summary  can  do  justice. 

With  a  grave  appearance  of  impartiality  he  declared  that  as  they 
were  now  finally  committing  themselves  to  Reform  or  Innovation,  it  was 


40  Flatland 

desirable  that  they  should  take  one  last  view  of  the  perimeter  of  the  whole 
subject,  its  defects  as  well  as  its  advantages.  Gradually  introducing  the 
mention  of  the  dangers  to  the  Tradesmen,  the  Professional  Classes  and  the 
Gentlemen,  he  silenced  the  rising  murmurs  of  the  Isosceles  by  reminding 
them  that,  in  spite  of  all  these  defects,  he  was  willing  to  accept  the  Bill  if 
it  was  approved  by  the  majority.  But  it  was  manifest  that  all,  except  the 
Isosceles,  were  moved  by  his  words  and  were  either  neutral  or  averse  to 
the  Bill. 

Turning  now  to  the  Workmen  he  asserted  that  their  interests  must  not 
be  neglected,  and  that,  if  they  intended  to  accept  the  Colour  Bill,  they 
ought  at  least  to  do  so  with  a  full  view  of  the  consequences.  Many  of 
them,  he  said,  were  on  the  point  of  being  admitted  to  the  class  of  the 
Regular  Triangles;  others  anticipated  for  their  children  a  distinction 
they  could  not  hope  for  themselves.  That  honourable  ambition  would 
now  have  to  be  sacrificed.  With  the  universal  adoption  of  Colour, 
all  distinctions  would  cease ;  Regularity  would  be  confused  with 
Irregularity  ;  development  would  give  place  to  retrogression ;  the 
Workman  would  in  a  few  generations  be  degraded  to  the  level  of  the 
Military,  or  even  the  Convict  Class;  political  power  would  be  in  the 
hands  of  the  greatest  number,  that  is  to  say  the  Criminal  Classes, 
who  were  already  more  numerous  than  the  Workmen,  and  would 
soon  out-number  all  the  other  Classes  put  together  when  the  usual 
Compensative  Laws  of  Nature  were  violated. 

A  subdued  murmur  of  assent  ran  through  the  ranks  of  the  Artisans, 
and  Chromatistes,  in  alarm,  attempted  to  step  forward  and  address  them. 
But  he  found  himself  encompassed  with  guards  and  forced  to  remain  silent 
while  the  Chief  Circle  in  a  few  impassioned  words  made  a  final  appeal  to 
the  Women,  exclaiming  that,  if  the  Colour  Bill  passed,  no  marriage  would 
henceforth  be  safe,  no  woman's  honour  secure ;  fraud,  deception,  hypocrisy 
would  pervade  every  household ;  domestic  bliss  would  share  the  fate  of  the 


Flat  land  41 

Constitution  and  pass  to  speedy  perdition.  Sooner  than  this,  he  cried 
"  Come  death." 

At  these  words,  which  were  the  preconcerted  signal  for  action,  the 
Isosceles  Convicts  fell  on  and  transfixed  the  wretched  Chromatistes ;  the 
Regular  Classes  opening  their  ranks,  made  way  for  a  band  of  Women 
who,  under  direction  of  the  Circles,  moved,  back  foremost,  invisibly  and 
unerringly  upon  the  unconscious  Soldiers  ;  the  Artisans,  imitating  the 
example  of  their  betters,  also  opened  their  ranks.  Meantime  bands  of 
Convicts  occupied  every  entrance  with  an  impenetrable  phalanx. 

The  battle,  or  rather  carnage,  was  of  short  duration.  Under  the 
skilful  generalship  of  the  Circles  almost  every  Woman's  charge  was  fatal, 
and  very  many  extracted  their  sting  uninjured,  ready  for  a  second 
slaughter.  But  no  second  blow  was  needed  ;  the  rabble  of  the  Isosceles 
did  the  rest  of  the  business  for  themselves.  Surprised,  leader-less,  attacked 
in  front  by  invisible  foes,  and  finding  egress  cut  off  by  the  Convicts  behind 
them,  they  at  once — after  their  manner — lost  all  presence  of  mind,  and 
raised  the  cry  of  "  treachery."  This  sealed  their  fate.  Every  Isosceles  now 
saw  and  felt  a  foe  in  every  other.  In  half  an  hour  not  one  of  that  vast 
multitude  was  living  ;  and  the  fragments  of  seven  score  thousand  of  the 
Criminal  Class  slain  by  one  another's  angles  attested  the  triumph  of  Order. 

The  Circles  delayed  not  to  push  their  victory  to  the  uttermost.  The 
Working  Men  they  spared  but  decimated.  The  Militia  of  the  Equilaterals 
was  at  once  called  out ;  and  every  Triangle  suspected  of  Irregularity  on 
reasonable  grounds,  was  destroyed  by  Court  Martial,  without  the  formality 
of  exact  measurement  by  the  Social  Board.  The  homes  of  the  Military 
and  Artisan  classes  were  inspected  in  a  course  of  visitations  extending 
through  upwards  of  a  year ;  and  during  that  period  every  town,  village, 
and  hamlet  was  systematically  purged  of  that  excess  of  the  lower  orders 
which  had  been  brought  about  by  the  neglect  to  pay  the  Tribute  of 
Criminals  to  the  Schools  and  University,  and  by  the  violation  of  the 

D 


42  Flatland 

other  natural  Laws  of  the  Constitution  of  Flatland.     Thus  the  balance  of 
classes  was  again  restored . 

Needless  to  say  that  henceforth  the  use  of  Colour  was  abolished,  and 
its  possession  prohibited.  Even  the  utterance  of  any  word  denoting 
Colour,  except  by  the  Circles  or  by  qualified  scientific  teachers,  was 
punished  by  a  severe  penalty.  Only  at  our  University  in  some  of  the 
very  highest  and  most  esoteric  classes — which  I  myself  have  never  been 
privileged  to  attend — it  is  understood  that  the  sparing  use  of  Colour  is 
still  sanctioned  for  the  purpose  of  illustrating  some  of  the  deeper  problems 
of  mathematics.  But  of  this  I  can  only  speak  from  hearsay. 

Elsewhere  in  Flatland,  Colour  is  now  non-existent.  The  art  of 
making  it  is  known  to  only  one  living  person,  the  Chief  Circle  for  the  time 
being ;  and  by  him  it  is  handed  down  on  his  death-bed  to  none  but  his 
Successor.  One  manufactory  alone  produces  it ;  and,  lest  the  secret 
should  be  betrayed,  the  Workmen  are  annually  consumed,  and  fresh  ones 
introduced.  So  great  is  the  terror  with  which  even  now  our  Aristocracy 
looks  back  to  the  far-distant  days  of  the  agitation  for  the  Universal 
Colour  Bill. 

§  ii. — Concerning  our  Priests. 

It  is  high  time  that  I  should  pass  from  these  brief  and  discursive 
notes  about  things  in  Flatland  to  the  central  event  of  this  book,  my 
initiation  into  the  mysteries  of  Space.  T/iat  is  my  subject ;  all  that 
has  gone  before  is  merely  preface. 

For  this  reason  I  must  omit  many  matters  of  which  the  explanation 
would  not,  I  flatter  myself,  be  without  interest  for  my  Readers  :  as  for 
example,  our  method  of  propelling  and  stopping  ourselves,  although 
destitute  of  feet ;  the  means  by  which  we  give  fixity  to  structures  of 
wood,  stone,  or  brick,  although  of  course  we  have  no  hands,  nor  can 
we  lay  foundations  as  you  can,  nor  avail  ourselves  of  the  lateral  pressure 


Flatland  43 

of  the  earth  ;  the  manner  in  which  the  rain  originates  in  the  intervals 
between  our  various  zones,  so  that  the  northern  regions  do  not  intercept 
the  moisture  from  falling  on  the  southern ;  the  nature  of  our  hills  and 
mines,  our  trees  and  vegetables,  our  seasons  and  harvests ;  our  Alphabet, 
and  method  of  writing,  adapted  to  our  linear  tablets  ;  these  and  a 
hundred  other  details  of  our  physical  existence  I  must  pass  over,  nor  do 
I  mention  them  now  except  to  indicate  to  my  readers  that  their  omission 
proceeds  not  from  forgetfulness  on  the  part  of  the  Author,  but  from 
his  regard  for  the  time  of  the  Reader. 

Yet  before  I  proceed  to  my  legitimate  subject  some  few  final  remarks 
will  no  doubt  be  expected  by  my  Readers  upon  those  pillars  and  mainstays 
of  the  Constitution  of  Flatland,  the  controllers  of  our  conduct  and 
shapers  of  our  destiny,  the  objects  of  universal  homage  and  almost  of 
adoration :  need  I  say  that  I  mean  our  Circles  or  Priests  ? 

When  I  call  them  Priests,  let  me  not  be  understood  as  meaning  no 
more  than  the  term  denotes  with  you.  With  us,  our  Priests  are  Adminis- 
trators of  all  Business,  Art,  and  Science  ;  Directors  of  Trade,  Commerce, 
Generalship,  Architecture,  Engineering,  Education,  Statesmanship,  Legis- 
lature, Morality,  Theology  ;  doing  nothing  themselves,  they  are  the 
Causes  of  everything,  worth  doing,  that  is  done  by  others. 

Although  popularly  every  one  called  a  Circle  is  deemed  a  Circle,  yet 
among  the  better  educated  Classes  it  is  known  that  no  Circle  is  really 
a  Circle,  but  only  a  Polygon  with  a  very  large  number  of  very  small 
sides.  In  proportion  to  the  number  of  the  sides  the  Polygon  approxi- 
mates to  a  Circle  ;  and,  when  the  number  is  very  great,  say  for  example 
three  or  four  hundred,  it  is  extremely  difficult  for  the  most  delicate  touch 
to  feel  any  polygonal  angles.  Let  me  say  rather,  it  would  be  difficult  : 
for,  as  I  have  shown  above,  Recognition  by  Feeling  is  unknown  among 
the  highest  society,  and  to  feel  a  Circle  would  be  considered  a  most 
audacious  insult.  This  habit  of  abstention  from  Feeling  in  the  best 

D  2 


44  Flatland 

society  enables  a  Circle  the  more  easily  to  sustain  the  veil  of  mystery  in 
which,  from  his  earliest  years,  he  is  wont  to  enwrap  the  exact  nature  of 
his  Perimeter  or  Circumference.  Three  feet  being  the  average  Perimeter 
it  follows  that,  in  a  Polygon  of  three  hundred  sides,  each  side  will  be 
no  more  than  the  hundredth  part  of  a  foot  in  length,  or  little  more  than 
the  tenth  part  of  an  inch ;  and  in  a  Polygon  of  six  or  seven  hundred 
sides  the  sides  are  little  larger  than  the  diameter  of  a  Spaceland  pin-head. 
It  is  always  assumed,  by  courtesy,  that  the  Chief  Circle  for  the  time  being 
has  ten  thousand  sides. 

The  ascent  of  the  posterity  of  the  Circles  in  the  social  scale  is  not 
restricted,  as  it  is  among  the  lower  Regular  classes,  by  the  Law  of  Nature 
which  limits  the  increase  of  eides  to  one  in  each  generation.  If  it  were 
so,  the  number  of  sides  in  a  Circle  would  be  a  mere  question  of  pedigree 
and  arithmetic,  and  the  four  hundred  and  ninety-seventh  descendant  of  an 
Equilateral  Triangle  would  necessarily  be  a  Polygon  with  five  hundred 
sides.  But  this  is  not  the  case.  Nature's  Law  prescribes  two  antagonistic 
decrees  affecting  Circular  propagation ;  first,  that  as  the  race  climbs 
higher  in  the  scale  of  development,  so  development  shall  proceed  at  an 
accelerated  pace  ;  second,  that  in  the  same  proportion,  the  race  shall 
become  less  fertile.  Consequently  in  the  home  of  a  Polygon  of  four 
or  five  hundred  sides  it  is  rare  to  find  a  son  ;  more  than  one  is  never 
seen.  On  the  other  hand  the  son  of  a  five-hundred-sided  Polygon 
has  been  known  to  possess  five  hundred  and  fifty,  or  even  six  hundred 
sides. 

Art  also  steps  in  to  help  the  process  of  the  higher  Evolution.  Our 
physicians  have  discovered  that  the  small  and  tender  sides  of  an  infant 
Polygon  of  the  higher  class  can  be  fractured,  and  his  whole  frame  re-set, 
with  such  exactness  that  a  Polygon  of  two  or  three  hundred  sides  some- 
times— by  no  means  always,  for  the  process  is  attended  with  serious  risk — 
but  sometimes  overleaps  two  or  three  hundred  generations,  and  as  it  were 


Flatland  45 

doubles  at  a  stroke,  the  number  of  his  progenitors  and  the  nobility 
of  his  descent. 

Many  a  promising  child  is  sacrificed  in  this  way.  Scarcely  one  out 
of  ten  survives.  Yet  so  strong  is  the  parental  ambition  among  those 
Polygons  who  are,  as  it  were,  on  the  fringe  of  the  Circular  class,  that  it  is 
very  rare  to  find  a  Nobleman  of  that  position  in  society,  who  has  neglected 
to  place  his  first-born  son  in  the  Circular  Neo-Therapeutic  Gymnasium 
before  he  has  attained  the  age  of  a  month. 

One  year  determines  success  or  failure.  At  the  end  of  that  time  the 
child  has,  in  all  probability,  added  one  more  to  the  tombstones  that 
crowd  the  Neo-Therapeutic  Cemetery;  but  on  rare  occasions  a  glad 
procession  bears  back  the  little  one  to  his  exultant  parents,  no  longer  a 
Polygon,  but  a  Circle,  at  least  by  courtesy  :  and  a  single  instance  of  so 
blessed  a  result  induces  multitudes  of  Polygonal  parents  to  submit  to 
similar  domestic  sacrifices,  which  have  a  dissimilar  issue. 

§    12. — Of  the   Doctrine  of  our   Priests. 

As  to  the  doctrine  of  the  Circles  it  may  briefly  be  summed  up  in  a 
single  maxim,  "Attend  to  your  Configuration."  Whether  political, 
ecclesiastical,  or  moral,  all  their  teaching  has  for  its  object  the  improve- 
ment of  individual  and  collective  Configuration — with  special  reference 
of  course  to  the  Configuration  of  the  Circles,  to  which  all  other  objects 
are  subordinated. 

It  is  the  merit  of  the  Circles  that  they  have  effectually  suppressed  those 
ancient  heresies  which  led  men  to  waste  energy  and  sympathy  in  the 
vain  belief  that  conduct  depends  upon  will,  effort,  training,  encourage- 
ment, praise,  or  anything  else  but  Configuration.  It  was  Pantocyclus — the 
illustrious  Circle  mentioned  above,  as  the  queller  of  the  Colour  Revolt — 
who  first  convinced  mankind  that  Configuration  makes  the  man  ;  that  if, 


46  Flatland 

for  example,  you  are  born  an  Isosceles  with  two  uneven  sides,  you  will 
assuredly  go  wrong  unless  you  have  them  made  even — for  which  purpose 
you  must  go  to  the  Isosceles  Hospital  ;  similarly,  if  you  are  a  Triangle,  or 
Square,  or  even  a  Polygon,  born  with  any  Irregularity,  you  must  be  taken 
to  one  of  the  Regular  Hospitals  to  have  your  disease  cured  ;  otherwise 
you  will  end  your  days  in  the  State  Prison  or  by  the  angle  of  the  State 
Executioner. 

All  faults  or  defects,  from  the  slightest  misconduct  to  the  most  flagitious 
crime,  Pantocyclus  attributed  to  some  deviation  from  perfect  Regularity  in 
the  bodily  figure,  caused  perhaps  (if  not  congenital)  by  some  collision  in 
a  crowd  ;  by  neglect  to  take  exercise,  or  by  taking  too  much  of  it ;  or 
even  by  a  sudden  change  of  temperature,  resulting  in  a  shrinkage  or 
expansion  in  some  too  susceptible  part  of  the  frame.  Therefore,  con- 
cluded that  illustrious  Philosopher,  neither  good  conduct  nor  bad  conduct 
is  a  fit  subject,  in  any  sober  estimation,  for  either  praise  or  blame.  For 
why  should  you  praise,  for  example,  the  integrity  of  a  Square  who  faith- 
fully defends  the  interests  of  his  client,  when  you  ought  in  reality  rather 
to  admire  the  exact  precision  of  his  Rectangles  ?  Or  again,  why  blame  a 
lying,  thievish  Isosceles  when  you  ought  rather  to  deplore  the  incurable 
inequality  of  his  sides  ? 

Theoretically,  this  doctrine  is  unquestionable ;  but  it  has  practical 
drawbacks.  In  dealing  with  an  Isosceles,  if  a  rascal  pleads  that  he 
cannot  help  stealing  because  of  his  unevenness,  you  reply  that  for  that 
very  reason,  because  he  cannot  help  being  a  nuisance  to  his  neighbours, 
you,  the  Magistrate,  cannot  help  sentencing  him  to  be  consumed — and 
there's  an  end  of  the  matter.  But  in  little  domestic  difficulties,  where 
the  penalty  of  consumption,  or  death,  is  out  of  the  question,  this 
theory  of  Configuration  sometimes  comes  in  awkwardly ;  and  I  must 
confess  that  occasionally  when  one  of  my  own  Hexagonal  Grandsons 
pleads  as  an  excuse  for  his  disobedience  that  a  sudden  change  of  the 


Flatland  47 

temperature  has  been  too  much  for  his  Perimeter,  and  that  I  ought  to  lay 
the  blame  not  on  him  but  on  his  Configuration,  which  can  only  be 
strengthened  by  abundance  of  the  choicest  sweetmeats,  I  neither  see  my 
way  logically  to  reject,  nor  practically  to  accept,  his  conclusions. 

For  my  own  part,  I  find  it  best  to  assume  that  a  good  sound  scolding  or 
castigation  has  some  latent  and  strengthening  influence  on  my  Grandson's 
Configuration  ;  though  I  own  that  I  have  no  grounds  for  thinking  so.  At 
all  events  I  am  not  alone  in  my  way  of  extricating  myself  from  this 
dilemma  ;  for  I  find  that  many  of  the  highest  Circles,  sitting  as  Judges  in 
Law  courts,  use  praise  and  blame  towards  Regular  and  Irregular  Figures  ; 
and  in  their  homes  I  know  by  experience  that,  when  scolding  their  children, 
they  speak  about  "  right "  or  "  wrong  "  as  vehemently  and  passionately  as 
if  they  believed  that  these  names  represented  real  existences,  and  that  a 
human  Figure  is  really  capable  of  choosing  between  them. 

Consistently  carrying  out  their  policy  of  making  Configuration  the  lead- 
ing idea  in  every  mind,  the  Circles  reverse  the  nature  of  that  Commandment 
which  in  Spaceland  regulates  the  relations  between  parents  and  children. 
With  you,  children  are  taught  to  honour  their  parents;  with  us — next  to  the 
Circles,  who  are  the  chief  object  of  universal  homage — a  man  is  taught  to 
honour  his  Grandson,  if  he  has  one;  or,  if  not,  his  Son.  By  "honour," how- 
ever, is  by  no  means  meant  "  indulgence,"  but  a  reverent  regard  for  their 
highest  interests :  and  the  Circles  teach  that  the  duty  of  fathers  is  to 
subordinate  their  own  interests  to  those  of  posterity,  thereby  advancing 
the  welfare  of  the  whole  State  as  well  as  that  of  their  own  immediate 
descendants. 

The  weak  point  in  the  system  of  the  Circles — if  a  humble  Square  may 
venture  to  speak  of  anything  Circular  as  containing  any  element  of  weak- 
ness— appears  to  me  to  be  found  in  their  relations  with  Women. 

As  it  is  of  the  utmost  importance  for  Society  that  Irregular  births  should 
be  discouraged,  it  follows  that  no  Woman  who  has  any  Irregularities  in  her 


48  Flatland 

ancestry  is  a  fit  partner  for  one  who  desires  that  his  posterity  should  rise 
by  regular  degrees  in  the  social  scale. 

Now  the  Irregularity  of  a  Male  is  a  matter  of  measurement ;  but  as 
all  Women  are  straight,  and  therefore  visibly  Regular  so  to  speak,  one  has 
to  devise  some  other  means  of  ascertaining  what  I  may  call  their  invisible 
Irregularity,  that  is  to  say  their  potential  Irregularities  as  regards  possible 
offspring.  This  is  effected  by  carefully-kept  pedigrees,  which  are  preserved 
and  supervised  by  the  State ;  and  without  a  certified  pedigree  no  Woman 
is  allowed  to  marry. 

Now  it  might  have  been  supposed  that  a  Circle — proud  of  his  ancestry 
and  regardful  for  a  posterity  which  might  possibly  issue  hereafter  in  a 
Chief  Circle — would  be  more  careful  than  any  other  to  choose  a  wife  who 
had  no  blot  on  her  escutcheon.  But  it  is  not  so.  The  care  in  choosing  a 
Regular  wife  appears  to  diminish  as  one  rises  in  the  social  scale.  Nothing 
would  induce  an  aspiring  Isosceles,  who  had  hopes  of  generating  an  Equi- 
lateral Son,  to  take  a  wife  who  reckoned  a  single  Irregularity  among  her 
Ancestors;  a  Square  or  Pentagon,  who  is  confident  that  his  family  is  steadily 
on  the  rise,  does  not  enquire  above  the  five-hundredth  generation  ;  a  Hex- 
agon or  Dodecahedron  is  even  more  careless  of  the  wife's  pedigree  ;  but  a 
Circle  has  been  known  deliberately  to  take  a  wife  who  has  had  an  Irregular 
Great-Grandfather,  and  all  because  of  some  slight  superiority  of  lustre,  or 
because  of  the  charms  of  a  low  voice — which,  with  us,  even  more  than  with 
you,  is  thought  "  an  excellent  thing  in  Woman." 

Such  ill-judged  marriages  are,  as  might  be  expected,  barren,  if  they  do 
not  result  in  positive  Irregularity  or  in  diminution  of  sides  ;  but  none  of 
these  evils  have  hitherto  proved  sufficiently  deterrent.  The  loss  of  a  few 
sides  in  a  highly-developed  Polygon  is  not  easily  noticed,  and  is  sometimes 
compensated  by  a  successful  operation  in  the  Neo-Therapeutic  Gymnasium, 
as  I  have  described  above  ;  and  the  Circles  are  too  much  disposed  to  acquiesce 
in  infecundity  as  a  Law  of  the  superior  development.  Yet,  if  this  evil  be 


Flatland  49 

not  arrested,  the  gradual  diminution  of  the  Circular  class  may  soon  become 
more  rapid,  and  the  time  may  be  not  far  distant  when,  the  race  being  no 
longer  able  to  produce  a  Chief  Circle,  the  Constitution  of  Flatland  must 
fall. 

One  other  word  of  warning  suggests  itself  to  me,  though  I  cannot  so 
easily  mention  a  remedy  ;  and  this  also  refers  to  our  relations  .with  Women. 
About  three  hundred  years  ago,  it  was  decreed  by  the  Chief  Circle  that, 
since  women  are  deficient  in  Reason  but  abundant  in  Emotion,  they  ought 
no  longer  to  be  treated  as  rational,  nor  receive  any  mental  education.  .[The 
consequence  was  that  they  were  no  longer  taught  to  read,  nor  even  to  master 
Arithmetic  enough  to  enable  them  to  count  the  angles  of  their  husband 
or  children ;  and  hence  they  sensibly  declined  during  each  generation  in 
intellectual  power.  And  this  system  of  female  non-education  or  quietism 
still  prevails. 

My  fear  is  that,  with  the  best  intentions,  this  policy  has  been  carried  so 
far  as  to  react  injuriously  on  the  Male  Sex. 

For  the  consequence  is  that,  as  things  now  are,  we  Males  have  to  lead  a 
kind  of  bi-lingual,  and  I  may  almost  say  bi-mental  existence.  With  the 
Women,  we  speak  of  " love,"  "duty,"  "right,"  "wrong,"  "pity,"  "hope," 
and  other  irrational  and  emotional  conceptions,  which  have  no  existence, 
and  the  fiction  of  which  has  no  object  except  to  control  feminine  exuber- 
ances ;  but  among  ourselves,  and  in  our  books,  we  have  an  entirely  different 
vocabulary  and  I  may  almost  say,  idiom.  "  Love  "  then  becomes  '  the  an- 
ticipation of  benefits  ; " . "  duty  "  becomes  "  necessity  "  or  "  fitness  ; "  and 
other  words  are  correspondingly  transmuted.  Moreover,  among  Women, 
we  use  language  implying  the  utmost  deference  for  their  Sex  ;  and  they 
fully  believe  that  the  Chief  Circle  Himself  is  not  more  devoutly  adored  by 
us  than  they  are  :  but  behind  their  backs  they  are  both  regarded  and  spoken 
of — by  all  except  the  very  young — as  being  little  better  than  "  mindless 
organisms." 


50  Flatland 

Our  Theology  also  in  the  Women's  chambers  is  entirely  different  from 
our  Theology  elsewhere. 

Now  my  humble  fear  is  that  this  double  training,  in  language  as  well 
as  in  thought,  imposes  somewhat  too  heavy  a  burden  upon  the  young, 
especially  when,  at  the  age  of  three  years  old,  they  are  taken  from  the 
maternal  care  and  taught  to  unlearn  the  old  language — except  for  the  pur- 
pose of  repeating  it  in  the  presence  of  their  Mothers  and  Nurses — and  to 
learn  the  vocabulary  and  idiom  of  science.  Already  methinks  I  discern  a 
weakness  in  the  grasp  of  mathematical  truth  at  the  present  time  as  com- 
pared with  the  more  robust  intellect  of  our  ancestors  three  hundred  years 
ago.  I  say  nothing  of  the  possible  danger  if  a  Woman  should  ever  sur- 
reptitiously learn  to  read  and  convey  to  her  Sex  the  result  of  her  perusal 
of  a  single  popular  volume  ;  nor  of  the  possibility  that  the  indiscretion  or 
disobedience  of  some  infant  Male  might  reveal  to  a  Mother  the  secrets  of 
the  logical  dialect.  On  the  simple  ground  of  the  enfeebling  of  the  Male 
intellect,  I  rest  this  humble  appeal  to  the  highest  Authorities  to  reconsider 
the  regulations  of  Female  Education. 


PART  II 
OTHER   WORLDS 

"  O  brave  new  worlds, 
That  have  such  people  in  them  ! " 


§    13. — How   I  had  a   Vision   of  Lineland. 

IT  was  the  last  day  but  one  of  the  1 999th  year  of  our  era,  and  the  first 
day  of  the  Long  Vacation.  Having  amused  myself  till  a  late  hour  with 
my  favourite  recreation  of  Geometry,  I  had  retired  to  rest  with  an  unsolved 
problem  in  my  mind.  In  the  night  I  had  a  dream. 

I  saw  before  me  a  vast  multitude  of  small  Straight  Lines  (which  I 
naturally  assumed  to  be  Women)  interspersed  with  other  Beings  still 
smaller  and  of  the  nature  of  lustrous  Points — all  moving  to  and  fro  in  one 
and  the  same  Straight  Line,  and,  as  nearly  as  I  could  judge,  with  the 
same  velocity. 


54  Plat  land 

A  noise  of  confused,  multitudinous  chirping  or  twittering  issued  from 
them  at  intervals  as  long  as  they  were  moving ;  but  sometimes  they 
ceased  from  motion,  and  then  all  was  silence. 

Approaching  one  of  the  largest  of  what  I  thought  to  be  Women,  I 
accosted  her,  but  received  no  answer.  A  second  and  third  appeal  on  my 
part  were  equally  ineffectual.  Losing  patience  at  what  appeared  to  me 
intolerable  rudeness,  I  brought  my  mouth  into  a  position  full  in  front  of 
her  mouth  so  as  to  intercept  her  motion,  and  loudly  repeated  my  question, 
"  Woman,  what  signifies  this  concourse,  and  this  strange  and  confused 
chirping,  and  this  monotonous  motion  to  and  fro  in  one  and  the  same 
Straight  Line?" 

"  I  am  no  Woman,"  replied  the  small  Line  ;  "  I  am  the  Monarch  of  the 
world.  But  thou,  whence  intrudest  thou  into  my  realm  of  Lineland  ? " 
Receiving  this  abrupt  reply,  I  begged  pardon  if  I  had  in  any  way  startled 
or  molested  his  Royal  Highness  ;  and  describing  myself  as  a  stranger  I 
besought  the  King  to  give  me  some  account  of  his  dominions.  But  I  had 
the  greatest  possible  difficulty  in  obtaining  any  information  on  points  that 
really  interested  me ;  for  the  Monarch  could  not  refrain  from  constantly 
assuming  that  whatever  was  familiar  to  him  must  also  be  known  to  me  and 
that  I  was  simulating  ignorance  in  jest.  However,  by  persevering  questions 
I  elicited  the  following  facts: 

It  seemed  that  this  poor  ignorant  Monarch — as  he  called  himself — was 
persuaded  that  the  Straight  Line  which  he  called  his  Kingdom,  and  in 
which  he  passed  his  existence,  constituted  the  whole  of  the  world,  and 
indeed  the  whole  of  Space.  Not  being  able  either  to  move  or  to  see,  save 
in  his  Straight  Line,  he  had  no  conception  of  anything  out  of  it.  Though 
he  had  heard  my  voice  when  I  first  addressed  him,  the  sounds  had  come  to 
him  in  a  manner  so  contrary  to  his  experience  that  he  had  made  no  answer, 
"  seeing  no  man,"  as  he  expressed  it,  "  and  hearing  a  voice  as  it  were  from 
my  own  intestines."  Until  the  moment  when  I  placed  my  mouth  in  his 


Flatland 


55 


World,  he  had  neither  seen  me,  nor  heard  anything  except  confused  sounds 
beating  against  what  I  called  his  side,  but  what  he  called  his  inside  or 
stomach ;  nor  had  he  even  now  the  least  conception  of  the  region  from 
which  I  had  come.  Outside  his  World,  or  Line,  all  was  a  blank  to  him  ; 
nay,  not  even  a  blank,  for  a  blank  implies  Space ;  say,  rather,  all  was 
non-existent. 

His  subjects — of  whom  the  small  Lines  were  Men  and  the  Points 
Women — were  all  alike  confined  in  motion  and  eye- sight  to  that  single 
Straight  Line,  which  was  their  World.  It  need  scarcely  be  added  that  the 
whole  of  their  horizon  was  limited  to  a  Point ;  nor  could  any  one  ever  see 
anything  but  a  Point.  Man,  woman,  child,  thing — each  was  a  Point  to  the 
eye  of  a  Linelander.  Only  by  the  sound  of  the  voice  could  sex  or  age  be 
distinguished.  Moreover,  as  each  individual  occupied  the  whole  of  the 
narrow  path,  so  to  speak,  which  constituted  his  Universe,  and  no  one  could 
move  to  the  right  or  left  to  make  way  for  passers  by,  it  followed  that  no 
Linelander  could  ever  pass  another.  Once  neighbours,  always  neighbours. 
Neighbourhood  with  them  was  like  marriage  with  us.  Neighbours  remained 
neighbours  till  death  did  them  part. 

Such  a  life,  with  all  vision  limited  to  a  Point,  and  all  motion  to  a  Straight 
Line,  seemed  to  me  inexpressibly  dreary ;  and  I  was  surprised  to  note  the 
vivacity  and  cheerfulness  of  the  King.  Wondering  whether  it  was  possible, 
amid  circumstances  so  unfavourable  to  domestic  relations,  to  enjoy  the 
pleasures  of  conjugal  union,  I  hesitated  for  some  time  to  question  his 
Royal  Highness  on  so  delicate  a  subject ;  but  at  last  I  plunged  into  it 
by  abruptly  inquiring  as  to  the  health  of  his  family.  "  My  wives  and 
children,"  he  replied,  "  are  well  and  happy." 

Staggered  at  this  answer — for  in  the  immediate  proximity  of  the 
Monarch  (as  I  had  noted  in  my  dream  before  I  entered  Lineland)  there 
were  none  but  Men — I  ventured  to  reply,  "  Pardon  me,  but  I  cannot 
imagine  how  your  Royal  Highness  can  at  any  time  either  see  or  approach 


56  Flatland 

their:  Majesties,  when  there  are  at  least  half  a  dozen  intervening  indi- 
viduals, whom  you  can  neither  see  through,  nor  pass  by  ?  Is  it  possible 
that  in  Lineland  proximity  is  not  necessary  for  marriage  and  for  the 
generation  of  children  ? " 

"How  can  you  ask  so  absurd  a  question  ?"  replied  the  Monarch.  "If 
it  were  indeed  as  you  suggest,  the  Universe  would  soon  be  depopulated. 
No,  no ;  neighbourhood  is  needless  for  the  union  of  hearts  ;  and  the  birth 
of  children  is  too  important  a  matter  to  have  been  allowed  to  depend  upon 
such  an  accident  as  proximity.  You  cannot  be  ignorant  of  this.  Yet 
since  you  are  pleased  to  affect  ignorance,  I  will  instruct  you  as  if  you 
were  the  veriest  baby  in  Lineland.  Know,  then,  that  marriages  are 
consummated  by  means  of  the  faculty  of  sound  and  the  sense  of  hearing. 

"  You  are  of  course  aware  that  every  Man  has  two  mouths  or  voices — 
as  well  as  two  eyes — a  bass  at  one  and  a  tenor  at  the  other  of  his  ex- 
tremities. I  should  not  mention  this,  but  that  I  have  been  unable  to 
distinguish  your  tenor  in  the  course  of  our  conversation."  I  replied  that 
I  had  but  one  voice,  and  that  I  had  not  been  aware  that  His  Royal 
Highness  had  two.  "  That  confirms  my  impression,"  said  the  King,  "  that 
you  are  not  a  Man,  but  a  feminine  Monstrosity  with  a  bass  voice  and  an 
utterly  uneducated  ear.  But  to  continue. 

"  Nature   herself  having  ordained  that  every  Man   should   wed  two 

wives "  Why  two  ? "  asked  I.     "  You  carry  your  affected  simplicity 

too  far,"  he  cried.  "  How  can  there  be  a  completely  harmonious  union 
without  the  combination  of  the  Four  in  One,  viz.  the  Bass  and  Tenor  of 
the  Man  and  the  Soprano  and  Contralto  of  the  two  Women  ? "  "  But 
supposing,"  said  I,  "  that  a  man  should  prefer  one  wife  or  three  ? "  "  It 
is  impossible,"  he  said ;  "  it  is  as  inconceivable  as  that  two  and  one  should 
make  five,  or  that  the  human  eye  should  see  a  Straight  Line."  I  would 
have  interrupted  him  ;  but  he  proceeded  as  follows  : 

"  Once  in  the  middle  of  each  week  a  Law  of  Nature  compels  us  to 


Flatland  57 

move  to  and  fro  with  a  rhythmic  motion  of  more  than  usual  violence,  which 
continues  for  the  time  you  would  take  to  count  a  hundred  and  one.  In  the 
midst  of  this  choral  dance,  at  the  fifty-first  pulsation,  the  inhabitants  of  the 
Universe  pause  in  full  career,  and  each  individual  sends  forth  his  richest, 
fullest,  sweetest  strain.  It  is  in  this  decisive  moment  that  all  our  marriages 
are  made.  So  exquisite  is  the  adaptation  of  Bass  to  Treble,  of  Tenor  to 
Contralto,  that  oftentimes  the  Loved  Ones,  though  twenty  thousand 
leagues  away,  recognise  at  once  the  responsive  note  of  their  destined 
Lover ;  and,  penetrating  the  paltry  obstacles  of  distance,  Love  unites  the 
three.  The  marriage  in  that  instant  consummated  results  in  a  threefold 
Male  and  Female  offspring  which  takes  its  place  in  Lineland. 

"  What !  Always  threefold  ? "  said  I.  "  Must  one  wife  then  always 
have  twins  ? " 

"  Bass-voiced  Monstrosity !  yes,"  replied  the  King.  "  How  else  could 
the  balance  of  the  Sexes  be  maintained,  if  two  girls  were  not  born  for 
every  boy  ?  Would  you  ignore  the  very  Alphabet  of  Nature  ? "  He 
ceased,  speechless  for  fury ;  and  some  time  elapsed  before  I  could  induce 
him  to  resume  his  narrative. 

"  You  will  not,  of  course,  suppose  that  every  bachelor  among  us  finds 
his  mates  at  the  first  wooing  in  this  universal  Marriage  Chorus.  On  the 
contrary,  the  process  is  by  most  of  us  many  times  repeated.  Few  are  the 
hearts  whose  happy  lot  it  is  at  once  to  recognise  in  each  other's  voices  the 
partner  intended  for  them  by  Providence,  and  to  fly  into  a  reciprocal  and 
perfectly  harmonious  embrace.  With  most  of  us  the  courtship  is  of  long 
duration.  The  Wooer's  voices  may  perhaps  accord  with  one  of  the  future 
wives,  but  not  with  both  ;  or  not,  at  first,  with  either  ;  or  the  Soprano  and 
Contralto  may  not  quite  harmonise.  In  such  cases  Nature  has  provided 
that  every  weekly  Chorus  shall  bring  the  three  Lovers  into  closer  harmony. 
Each  trial  of  voice,  each  fresh  discovery  of  discord,  almost  imperceptibly 
induces  the  less  perfect  to  modify  his  or  her  vocal  utterance  so  as  to 

E 


58  Flatland 

approximate  to  the  more  perfect.  And  after  many  trials  and  many  ap- 
proximations, the  result  is  at  last  achieved.  There  comes  a  day  at  last, 
when,  while  the  wonted  Marriage  Chorus  goes  forth  from  universal 
Lineland,  the  three  far-off  Lovers  suddenly  find  themselves  in  exact 
harmony,  and,  before  they  are  aware,  the  wedded  Triplet  is  rapt  vocally 
into  a  duplicate  embrace ;  and  Nature  rejoices  over  one  more  marriage  and 
over  three  more  births. " 

§  14. — How  I  vainly  tried  to  explain  the  nature  of  Flatland. 

Thinking  that  it  was  time  to  bring  down  the  Monarch  from  his  raptures 
to  the  level  of  common  sense,  I  determined  to  endeavour  to  open  up  to 
him  some  glimpses  of  the  truth,  that  is  to  say  of  the  nature  of  things  in 
Flatland.  So  I  began  thus  :  "  How  does  your  Royal  Highness  distinguish 
the  shapes  and  positions  of  his  subjects  ?  I  for  my  part  noticed  by  the 
sense  of  sight,  before  I  entered  your  Kingdom,  that  some  of  your  people 

are  Lines  and  others  Points,  and  that  some  of  the  Lines  are  larger " 

"  You  speak  of  an  impossibility,"  interrupted  the  King  ;  "  you  must  have 
seen  a  vision  ;  for  to  detect  the  difference  between  a  Line  and  a  Point  by 
the  sense  of  sight  is,  as  every  one  knows,  in  the  nature  of  things,  impossible  ; 
but  it  can  be  detected  by  the  sense  of  hearing,  and  by  the  same  means  my 
shape  can  be  exactly  ascertained.  Behold  me — I  am  a  Line,  the  longest  in 

Lineland,  over  six  inches  of  Space "  "  Of  Length,"  I  ventured  to  suggest. 

"  Fool,"  said  he,  "  Space  is  Length.  Interrupt  me  again,  and  I  have 
done." 

I  apologised;  but  he  continued  scornfully,  "Since  you  are  impervious 
to  argument,  you  shall  hear  with  your  ears  how  by  means  of  my  two 
voices  I  reveal  my  shape  to  my  Wives,  who  are  at  this  moment  six 
thousand  miles  seventy  yards  two  feet  eight  inches  away,  the  one  to 
the  North,  the  other  to  the  South.  Listen,  I  call  to  them." 


Flatland 


59 


He  chirruped,  and  then  complacently  continued  :  "  My  wives  at  this 
moment  receiving  the  sound  of  one  of  my  voices,  closely  followed  by  the 
other,  and  perceiving  that  the  latter  reaches  them  after  an  interval  in  which 
sound  can  traverse  6*457  inches,  infer  that  one  of  my  mouths  is  6*457 
inches  further  from  them  than  the  other,  and  accordingly  know  my  shape 
to  be  6*457  inches.  But  you  will  of  course  understand  that  my  wives 
do  not  make  this  calculation  every  time  they  hear  my  two  voices.  They 
made  it,  once  for  all,  before  we  were  married.  But  they  could  make 
it  at  any  time.  And  in  the  same  way  I  can  estimate  the  shape  of 
any  of  my  Male  subjects  by  the  sense  of  sound," 

"  But  how,"  said  I,  "  if  a  Man  feigns  a  Woman's  voice  with  one 
of  his  two  voices,  or  so  disguises  his  Southern  voice  that  it  cannot  be 
recognised  as  the  echo  of  the  Northern  ?  May  not  such  deceptions 
cause  great  inconvenience  ?  And  have  you  no  means  of  checking  frauds 
of  this  kind  by  commanding  your  neighbouring  subjects  to  feel  one 
another  ? "  This  of  course  was  a  very  stupid  question,  for  feeling  could 
not  have  answered  the  purpose ;  but  I  asked  with  the  view  of  irritating 
the  Monarch,  and  I  succeeded  perfectly. 

"  What !  "  cried  he  in  horror,  "  explain  your  meaning."  "  Feel,  touch, 
come  into  contact,"  I  replied.  "  If  you  mean  by  feeling"  said  the  King, 
"approaching  so  close  as  to  leave  no  space  between  two  individuals, 
know,  Stranger,  that  this  offence  is  punishable  in  my  dominions  by  death. 
And  the  reason  is  obvious.  The  frail  form  of  a  Woman,  being  liable  to  be 
shattered  by  such  an  approximation,  must  be  preserved  by  the  State  ; 
but  since  Women  cannot  be  distinguished  by  the  sense  of  sight  from 
Man,  the  Law  ordains  universally  that  neither  Man  nor  Woman  shall  be 
approached  so  closely  as  to  destroy  the  interval  between  the  approximator 
and  the  approximated. 

"And  indeed  what  possible  purpose  would  be  served  by  this  illegal 
and  unnatural  excess  of  approximation  which  you  call  touching,  when 

E  2 


60  Flatland 

all  the  ends  of  so  brutal  and  coarse  a  process  are  attained  at  once  more 
easily  and  more  exactly  by  the  sense  of  hearing.  As  to  your  suggested 
danger  of  deception,  it  is  non-existent :  for  the  Voice,  being  the  essence  of 
one's  Being,  cannot  be  thus  changed  at  will.  But  come,  suppose  that 
I  had  the  power  of  passing  through  solid  things,  so  that  I  could  penetrate 
my  subjects,  one  after  another,  even  to  the  number  of  a  billion, 
verifying  the  size  and  distance  of  each  by  the  sense  of  feeling:  how 
much  time  and  energy  would  be  wasted  in  this  clumsy  and  inaccurate 
method !  Whereas  now,  in  one  moment  of  audition,  I  take  as  it  were  the 
census  and  statistics,  local,  corporal,  mental,  and  spiritual,  of  every  living 
being  in  Lineland.  Hark,  only  hark  ! " 

So  saying  he  paused  and  listened,  as  if  in  an  ecstasy,  to  a  sound 
which  seemed  to  me  no  better  than  a  tiny  chirping  from  an  innumerable 
multitude  of  lilliputian  grasshoppers. 

"  Truly,"  replied  I,  "  your  sense  of  hearing  serves  you  in  good  stead, 
and  fills  up  many  of  your  deficiencies.  But  permit  me  to  point  out 
that  your  life  in  Lineland  must  be  deplorably  dull.  To  see  nothing  but 
a  Point !  Not  even  to  be  able  to  Contemplate  a  Straight  Line  !  Nay,  not 
even  to  know  what  a  Straight  Line  is !  To  see,  yet  to  be  cut  off  from 
those  Linear  prospects  which  are  vouchsafed  to  us  in  Flatland  !  Better 
surely  to  have  no  sense  of  sight  at  all  than  to  see  so  little !  I 
grant  you  I  have  not  your  discriminative  faculty  of  hearing  ;  for  the 
concert  of  all  Lineland  which  gives  you  such  intense  pleasure,  is  to 
me  no  better  than  a  multitudinous  twittering  or  chirping.  But  at 
least  I  can  discern,  by  sight,  a  Line  from  a  Point.  And  let  me  prove 
it.  Just  before  I  Came  into  your  kingdom,  I  saw  you  dancing  from 
left  to  right,  and  then  from  right  to  left,  with  seven  Men  and  a  Woman 
in  your  immediate  proximity  on  the  left,  and  eight  Men  and  two  Women 
on  your  right.  Is  not  this  correct  ?  " 

"It  is  correct,"  said  the  King,  "so  far  as  the  numbers  and  sexes  are 


Flat  land  61 

concerned,  though  I  know  not  what  you  mean  by  '  right '  and  '  left.' 
But  I  deny  that  you  saw  these  things.  For  how  could  you  see  the  Line, 
that  is  to  say  the  inside,  of  any  Man  ?  But  you  must  have  heard  these 
things,  and  then  dreamed  that  you  saw  them.  And  let  me  ask  what  you 
mean  by  those  words  '  left '  and  '  right.'  I  suppose  it  is  your  way  of 
saying  Northward  and  Southward." 

"  Not  so,"  replied  I  ;  "  besides  your  motion  of  Northward  and 
Southward,  there  is  another  motion  which  I  call  from  right  to  left." 

King.  Exhibit  to  me,  if  you  please,  this  motion  from  left  to 
right. 

/.  Nay,  that  I  cannot  do,  unless  you  could  step  out  of  your  Line 
altogether. 

King.  Out  of  my  Line  ?  Do  you  mean  out  of  the  World  ?  Out 
of  Space  ? 

/.  Well,  yes.  Out  of  your  World.  Out  of  your  Space.  For  your 
Space  is  not  the  true  Space.  True  Space  is  a  Plane ;  but  your  Space 
is  only  a  Line. 

King.  If  you  cannot  indicate  this  motion  from  left  to  right  by 
yourself  moving  in  it,  then  I  beg  you  to  describe  it  to  me  in  words. 

/.  If  you  cannot  tell  your  right  side  from  my  left,  I  fear  that  no  words 
of  mine  can  make  my  meaning  clear  to  you.  But  surely  you  cannot  be 
ignorant  of  so  simple  a  distinction. 

King.  I  do  not  in  the  least  understand  you. 

/.  Alas  !  How  shall  I  make  it  clear  ?  When  you  move  straight  on, 
does  it  not  sometimes  occur  to  you  that  you  could  move  in  some  other 
way,  turning  your  eye  round  so  as  to  look  in  the  direction  towards 
which  your  side  is  now  fronting  ?  In  other  words,  instead  of  always 
moving  in  the  direction  of  one  of  your  extremities,  do  you  never  feel  a 
desire  to  move  in  the  direction,  so  to  speak,  of  your  side  ? 

King.   Never.     And  what  do  you  mean  ?     How  can  a   man's  inside 


62  Flatland 

"front"   in   any   direction?     Or   how   can  a  man  move  in  the  direction 
of  his  inside  ? 

/.  Well  then,  since  words  cannot  explain  the  matter,  I  will  try  deeds, 
and  will  move  gradually  out  of  Lineland  in  the  direction  which  I 
desire  to  indicate  to  you. 

At  the  word  I  began  to  move  my  body  out  of  Lineland.  As  long  as 
any  part  of  me  remained  in  his  dominion  and  in  his  view,  the  King 

kept  exclaim- 
ing, "  I  see 
you,  I  see  you 
still ;  you  are 
not  moving." 
But  when  I 

had  at  last  moved  myself  out  of  his  Line,  he  cried  in  his  shrillest  voice, 
"  She  is  vanished ;  she  is  dead."  "  I  am  not  dead,"  replied  I  ;  "I  am 
simply  out  of  Lineland,  that  is  to  say,  out  of  the  Straight  Line  which  you 
call  Space,  and  in  the  true  Space,  where  I  can  see  things  as  they  are. 
And  at  this  moment  I  can  see  your  Line,  or  side — or  inside  as  you  are 
pleased  to  call  it ;  and  I  can  also  see  the  Men  and  Women  on  the  North 
and  South  of  you,  whom  I  will  now  enumerate,  describing  their  order,  their 
size,  and  the  interval  between  each," 

When  I  had  done  this  at  great  length,  I  cried  triumphantly,  "  Does 
this  at  last  convince  you  ? "  And,  with  that,  I  once  more  entered 
Lineland,  taking  up  the  same  position  as  before. 

But  the  Monarch  replied,  "  If  you  were  a  Man  of  sense-^-though,  as  you 
appear  to  have  only  one  voice  I  have  little  doubt  you  are  not  a  Man  but  a 
Woman — but,  if  you  had  a  particle  of  sense,  you  would  listen  to  reason. 
You  ask  me  to  believe  that  there  is  another  Line  besides  that  which  my 
senses  indicate,  and  another  motion  besides  that  of  which  I  am  daily 
conscious.  I,  in  return,  ask  you  to  describe  in  words  or  indicate  by 


Flatland  63 

motion  that  other  Line  of  which  you  speak.  Instead  of  moving,  you 
merely  exercise  some  magic  art  of  vanishing  and  returning  to  sight ;  and 
instead  of  any  lucid  description  of  your  new  World,  you  simply  tell  me  the 
numbers  and  sizes  of  some  forty  of  my  retinue,  facts  known  to  any 
child  in  my  capital.  Can  anything  be  more  irrational  or  audacious  ? 
Acknowledge  your  folly  or  depart  from  my  dominions." 

Furious  at  his  perversity,  and  especially  indignant  that  he  professed  to 
be  ignorant  of  my  Sex,  I  retorted  in  no  measured  terms,  "  Besotted  Being ! 
You  think  yourself  the  perfection  of  existence,  while  you  are  in  reality 
the  most  imperfect  and' imbecile.  You  profess  to  see,  whereas  you  can  see 
nothing  but  a  Point !  You  plume  yourself  on  inferring  the  existence  of  a 
Straight  Line;  but  I  can  see  Straight  Lines  and  infer  the  existence  of 
Angles,  Triangles,  Squares,  Pentagons,  Hexagons,  and  even  Circles.  Why 
waste  more  words  ?  suffice  it  that  I  am  the  completion  of  your  incomplete 
self.  You  are  a  Line,  but  I  am  a  Line  of  Lines,  called  in  my  country 
a  Square :  and  even  I,  infinitely  superior  though  I  am  to  you,  am  of  little 
account  among  the  great  Nobles  of  Flatland,  whence  I  have  come  to 
visit  you,  in  the  hope  of  enlightening  your  ignorance." 

Hearing  these  words  the  King  advanced  towards  me  with  a  menacing 
cry  as  if  to  pierce  me  through  the  diagonal ;  and  in  that  same  moment 
there  arose  from  myriads  of  his  subjects  a  multitudinous  war-cry, 
increasing  in  vehemence  till  at  last  methpught  it  rivalled  the  roar  of 
an  army  of  a  hundred  thousand  Isosceles,  and  the  artillery  of  a 
thousand]  Pentagons.  Spell-bound  and  motionless  I  could  neither 
speak  nor  move  to  avert  the  impending  destruction ;  and  still  the 
noise  grew  louder,  and  the  King  came  closer,  when  I  awoke  to  find 
the  breakfast-bell  recalling  me  to  the  realities  of  Flatland, 


64  Flat  land 


§    15. — Concerning  a  Stranger  from  Spac  eland. 

From  dreams  I  proceed  to  facts. 

It  was  the  last  day  of  the  1999^1  year  of  our  era.  The  pattering  of 
the  rain  had  long  ago  announced  nightfall ;  and  I  was  sitting 1  in  the 
company  of  my  wife,  musing  on  the  events  of  the  past  and  the  prospects 
of  the  coming  year,  the  coming  century,  the  coming  Millennium. 

My  four  Sons  and  two  orphan  Grandchildren  had  retired  to  their 
several  apartments ;  and  my  Wife  alone  remained  with  me  to  see  the  old 
Millennium  out  and  the  new  one  in. 

I  was  rapt  in  thought,  pondering  in  my  mind  some  words  that  had 
casually  issued  from  the  mouth  of  my  youngest  Grandson,  a  most  promising 
young  Hexagon  of  unusual  brilliancy  and  perfect  angularity.  His  uncles 
and  I  had  been  giving  him  his  usual  practical  lesson  in  Sight  Recognition, 
turning  ourselves  upon  our  centres,  now  rapidly,  now  more  slowly,  and 
questioning  him  as  to  our  positions ;  and  his  answers  had  been  so  satis- 
factory that  I  had  been  induced  to  reward  him  by  giving  him  a  few  hints 
on  Arithmetic,  as  applied  to  Geometry. 

Taking  nine  Squares,  each  an  inch  every  way,  I  had  put  them  together 
so  as  to  make  one  large  Square,  with  a  side  of  three  inches,  and  I  had 
hence  proved  to  my  little  Grandson  that — though  it  was  impossible  for  us 
to  see  the  inside  of  the  Square — yet  we  might  ascertain  the  number  of 
square  inches  in  a  Square  by  simply  squaring  the  number  of  inches 

1  When  I  say  "  sitting,"  of  course  I  do  not  mean  any  change  of  attitude  such  as  you  in  Flatland 
signify  by  that  word  ;  for  as  we  have  no  feet,  we  can  no  more  "sit "  nor  " stand  "  (in  your  sense  of 
the  word)  than  one  of  your  soles  or  flounders. 

Nevertheless,  we  perfectly  well  recognise  the  different  mental  states  of  volition  implied  in 
"  tying>"  "sitting,"  and  "  standing,"  which  are  to  some  extent  indicated  to  a  beholder  by  a  slight 
increase  of  lustre  corresponding  to  the  increase  of  volition. 

But  on  this,  and  a  thousand  other  kindred  subjects,  time  forbids  me  to  dwell. 


Flatland  65 

, 

in  the  side  :  "  and  thus,"  said  I,  "  we  know  that  y,  or  9,  represents  the 
number  of  square  inches  in  a  Square  whose  side  is  3  inches  long." 

The  little  Hexagon  meditated  on  this  awhile  and  then  said  jo  me:  "But 
you  have  been  teaching  me  to  raise  numbers  to  the  third  power  ;  I  suppose 
33  must  mean  something  in  Geometry  ;  what  does  it  mean  ?  "  "  Nothing 
at  all,"  replied  I,  "  not  at  least  in  Geometry ;  for  Geometry  has  only  Two 
Dimensions."  And  then  I  began  to  show  the  boy  how  a  Point  by  moving 
through  a  length  of  three  inches  makes  a  Line  of  three  inches,  which  may 
be  represented  by  3  ;  and  how  a  Line  of  three  inches,  moving  parallel  to 
itself  through  a  length  of  three  inches,  makes  a  Square  of  three  inches 
every  way,  which  may  be  represented  by  y. 

Upon  this,  my  Grandson,  again  returning  to  his  former  suggestion,  took 
me  up  rather  suddenly  and  exclaimed,  "  Well,  then,  if  a  Point  by  moving 
three  inches,  makes  a  Line  of  three  inches  represented  by  3  ;  and  if  a  straight 
Line  of  three  inches,  moving  parallel  to  itself,  makes  a  Square  of  three 
inches  every  way,  represented  by  32 ;  it  must  be  that  a  Square  of  three 
inches  every  way,  moving  somehow  parallel  to  itself  (but  I  don't  see  how) 
must  make  a  Something  else  (but  I  don't  see  what)  of  three  inches  every 
way — and  this  must  be  represented  by  33." 

"  Go  to  bed,"  said  I,  a  little  ruffled  by  his  interruption  ;  "  if  you  would 
talk  less  nonsense,  you  would  remember  more  sense." 

So  my  Grandson  had  disappeared  in  disgrace  ;  and  there  I  sat  by  my 
Wife's  side,  endeavouring  to  form  a  retrospect  of  the  year  1999  and  of  the 
possibilities  of  the  year  2000,  but  not  quite  able  to  shake  off  the  thoughts 
suggested  by  the  prattle  of  my  bright  little  Hexagon.  Only  a  few  sands 
now  remained  in  the  half-hour  glass.  Rousing  myself  from  my  reverie  I 
turned  the  glass  Northward  for  the  last  time  in  the  old  Millennium ;  and  in 
the  act,  I  exclaimed  aloud,  "  The  boy  is  a  fool." 

Straightway  I  became  conscious  of  a  Presence  in  the  room,  and  a 
chilling  breath  thrilled  through  my  very  being.  "  He  is  no  such  thing," 


66  Flatland 

cried  my  Wife,  "and  you  are  breaking  the  Commandments  in  thus  dis- 
honouring your  own  Grandson."  But  I  took  no  notice  of  her.  Looking 
round  in  every  direction  I  could  see  nothing ;  yet  still  I  felt  a  Presence, 
and  shivered  as  the  cold  whisper  came  again.  I  started  up.  "  What  is 
the  matter  ? "  said  my  Wife,  "  there  is  no  draught ;  what  are  you 
looking  for  ?  There  is  nothing."  There  was  nothing  ;  and  I  resumed 
my  seat,  again  exclaiming,  "  The  boy  is  a  fool,  I  say ;  33  can  have  no 
meaning  in  Geometry."  At  once  there  came  a  distinctly  audible  reply, 
"  The  boy  is  not  a  fool ;  and  33  has  an  obvious  Geometrical  meaning." 

My  Wife  as  well  as  myself  heard  the  words,  although  she  did  not 
understand  their  meaning,  and  both  of  us  sprang  forward  in  the  direction 
of  the  sound.  What  was  our  horror  when  we  saw  before  us  a  Figure ! 
At  the  first  glance  it  appeared  to  be  a  Woman,  seen  sideways  ;  but  a 
moment's  observation  shewed  me  that  the  extremities  passed  into  dimness 
too  rapidly  to  represent  one  of  the  Female  Sex;  and  I  should  have 
thought  it  a  Circle,  only  that  it  seemed  to  change  its  size  in  a  manner 
impossible  for  a  Circle  or  for  any  Regular  Figure  of  which  I  had  had 
experience. 

But  my  Wife  had  not  my  experience,  nor  the~  coolness  necessary  to 
note  these  characteristics.  With  the  usual  hastiness  and  unreasoning 
jealousy  of  her  Sex,  she  flew  at  once  to  the  conclusion  that  a  Woman 
had  entered  the  house  through  some  small  aperture.  "  How  comes  this 
person  here?"  she  exclaimed,  "you  promised  me,  my  dear,  that  there 
should  be  no  ventilators  in  our  new  house."  "  Nor  are  there  any,"  said  I ; 
"  but  what  makes  you  think  that  the  stranger  is  a  Woman  ?  I  see  by  my 

power  of  Sight  Recognition "  "  Oh,  I  have  no  patience  with  your 

Sight  Recognition,"  replied  she,  "  '  Feeling  is  believing '  and  '  A  Straight 
Line  to  the  touch  is  worth  a  Circle  to  the  sight ' " — two  Proverbs,  very 
common  with  the  Frailer  Sex  in  Flatland. 

"Well,"  said  I,  for   I  was  afraid  of  irritating  her,  "if  it  must  be  so, 


Flatland  67 

demand  an  introduction."  Assuming  her  most  gracious  manner,  my  Wife 
advanced  towards  the  Stranger,  "  Permit  me,  Madam,  to  feel  and  be  felt 

by "  then,  suddenly  recoiling,  "  Oh  !  it  is  not  a  Woman,  and  there 

are  no  angles  either,  not  a  trace  of  one.  Can  it  be  that  I  have  so 
misbehaved  to  a  perfect  Circle  ? " 

"  I  am  indeed,  in  a  certain  sense  a  Circle,"  replied  the  Voice,  "and  a 
more  perfect  Circle  than  any  in  Flatland  ;  but  to  speak  more  accurately, 
I  am  many  Circles  in  one."  Then  he  added  more  mildly,  "  I  have  a 
message,  dear  Madam,  to  your  husband,  which  I  must  not  deliver  in 

your  presence  ;  arid,  if  )rou  would  suffer  us  to  retire  for  a  few  minutes ' 

But  my  Wife  would  not  listen  to  the  proposal  that  our  august  Visitor  should 
so  incommode  himself,  and  assuring  the  Circle  that  the  hour  for  her  own 
retirement  had  long  passed,  with  many  reiterated  apologies  for  her  recent 
indiscretion,  she  at  last  retreated  to  her  apartment. 

I  glanced  at  the  half-hour  glass.  The  last  sands  had  fallen.  The 
second  Millennium  had  begun, 

§   1 6. — How   the   Stranger   vainly    endeavoured    to    reveal  to    me  in 
words  the   mysteries   of  Sfiaceland. 

As  soon  as  the  sound  of  my  Wife's  retreating  footsteps  had  died  away, 
I  began  to  approach  the  Stranger  with  the  intention  of  taking  a  nearer 
view  and  of  bidding  him  be  seated :  but  his  appearance  struck  me  dumb 
and  motionless  with  astonishment.  Without  the  slightest  symptoms  of 
angularity  he  nevertheless  varied  every  instant  with  gradations  of  size 
and  brightness  scarcely  possible  for  any  Figure  within  the  scope  of  my 
experience.  The  thought  flashed  across  me  that  I  might  have  before  me 
a  burglar  or  cut-throat,  some  monstrous  Irregular  Isosceles,  who,  by 
feigning  the  voice  of  a  Circle,  had  obtained  admission  somehow  into  the 
house,  and  was  now  preparing  to  stab  me  with  his  acute  angle. 


68  Flatland 

In  a  sitting-room,  the  absence  of  Fog  (and  the  season  happened  to  be 
remarkably  dry),  made  it  difficult  for  me  to  trust  to  Sight  Recognition, 
especially  at  the  short  distance  at  which  I  was  standing.  Desperate  with 
fear,  I  rushed  forward  with  an  unceremonious  "  You  must  permit  me, 
Sir — "  and  felt  him.  My  Wife  was  right.  There  was  not  the  trace  of  an 
angle,  not  the  slightest  roughness  or  inequality :  never  in  my  life  had 
I  met  with  a  more  perfect  Circle.  He  remained  motionless  while  I 
walked  round  him,  beginning  from  his  eye  and  returning  to  it  again. 
Circular  he  was  throughout,  a  perfectly  satisfactory  Circle;  there  could 
not  be  a  doubt  of  it.  Then  followed  a  dialogue,  which  I  will  endeavour 
to  set  down  as  near  as  I  can  recollect  it,  omitting  only  some  of  my 
profuse  apologies — for  I  was  covered  with  shame  and  humiliation  that  I, 
a  Square,  should  have  been  guilty  of  the  impertinence  of  feeling  a 
Circle.  It  was  commenced  by  the  Stranger  with  some  impatience  at 
the  lengthiness  of  my  introductory  process. 

Stranger.  Have  you  felt  me  enough  by  this  time  ?  Are  you  not 
introduced  to  me  yet  ? 

/.  Most  illustrious  Sir,  excuse  my  awkwardness,  which  arises  not  from 
ignorance  of  the  usages  of  polite  society,  but  from  a  little  surprise  and 
nervousness,  consequent  on  this  somewhat  unexpected  visit.  And  I 
beseech  you  to  reveal  my  indiscretion  to  no  one,  and  especially  not  to 
my  Wife.  But  before  your  Lordship  enters  into  further  communications, 
would  he  deign  to  satisfy  the  curiosity  of  one  who  would  gladly  know 
whence  his  Visitor  came  ? 

Stranger.  From  Space,  from  Space,  Sir :  whence  else  ? 

/.  Pardon  me,  my  Lord,  but  is  not  your  Lordship  already  in  Space, 
your  Lordship  and  his  humble  servant,  even  at  this  moment  ? 

Stranger.  Pooh  !  what  do  you  know  of  Space  ?     Define  Space. 

/.  Space,  my  Lord,  is  height  and  breadth  indefinitely  prolonged. 

Stranger.  Exactly  :   you  see  you  do  not  even  know  what  Space  is. 


Flatland  69 

You  think  it  is  of  Two  Dimensions  only ;  but  I  have  come  to  announce 
to  you  a  Third — height,  breadth,  and  length. 

/.  Your  Lordship  is  pleased  to  be  merry.  We  also  speak  of  length 
and  height,  or  breadth  and  thickness,  thus  denoting  Two  Dimensions  by 
four  names. 

Stranger.  But  I  mean  not  only  three  names,  but  Three  Dimensions. 

/.  Would  your  Lordship  indicate  or  explain  to  me  in  what  direction 
is  the  Third  Dimension,  unknown  to  me  ? 

Stranger.  I  came  from  it.     It  is  up  above  and  down  below. 

/.  My  Lord  means  seemingly  that  it  is  Northward  and  Southward. 

Stranger.  I  mean  nothing  of  the  kind.  I  mean  a  direction  in  which 
you  cannot  look,  because  you  have  no  eye  in  your  side. 

/.  Pardon  me,  my  Lord,  a  moment's  inspection  will  convince  your 
Lordship  that  I  have  a  perfect  luminary  at  the  juncture  of  two  of 
my  sides. 

Stranger.  Yes :  but  in  order  to  see  into  Space  you  ought  to  have  an 
eye,  not  on  your  Perimeter,  but  on  your  side,  that  is,  on  what  you  would 
probably  call  your  inside ;  but  we  in  Spaceland  should  call  it  your  side. 

/.  An  eye  in  my  inside  !   An  eye  in  my  stomach  !   Your  Lordship  jests. 

Stranger.  I  am  in  no  jesting  humour.  I  tell  you  that  I  come 
from  Space,  or,  since  you  will  not  understand  what  Space  means,  from 
the  Land  of  Three  Dimensions  whence  I  but  lately  looked  down  upon 
your  Plane  which  you  call  Space  forsooth.  From  that  position  of 
advantage  I  discerned  all  that  you  speak  of  as  solid  (by  which  you 
mean  "  enclosed  on  four  sides  "),  your  houses,  your  churches,  your  very 
chests  and  safes,  yes  even  your  insides  and  stomachs,  all  lying  open  and 
exposed  to  my  view. 

/.  Such  assertions  are  easily  made,  my  Lord. 

Stranger.  But  not  easily  proved,  you  mean.  But  I  mean  to 
prove  mine. 


70  Flatland 

When  I  descended  here,  I  saw  your  four  Sons,  the  Pentagons,  each  in 
his  apartment,  and  your  two  Grandsons  the  Hexagons ;  I  saw  your 
youngest  Hexagon  remain  a  while  with  you  and  then  retire  to  his  room, 
leaving  you  and  your  Wife  alone.  I  saw  your  Isosceles  servants,  three 
in  number,  in  the  kitchen  at  supper,  and  the  little  Page  in  the  scullery. 
Then  I  came  here,  and  how  do  you  think  I  came  ? 

/.  Through  the  roof,  I  suppose. 

Stranger.  Not  so.  Your  roof,  as  you  know  very  well,  has  been 
recently  repaired,  and  has  no  aperture  by  which  even  a  Woman  could 
penetrate.  I  tell  you  I  come  from  Space.  Are  you  not  convinced  by 
what  I  have  told  you  of  your  children  and  household. 

/.  Your  Lordship  must  be  aware  that  such  facts  touching  the  belong- 
ings of  his  humble  servant  might  be  easily  ascertained  by  any  one  in 
the  neighbourhood  possessing  your  Lordship's  ample  means  of  obtaining 
information. 

Stranger.  How  shall  I  convince  him  ?  Surely  a  plain  statement 
of  facts  followed  by  ocular  demonstration  ought  to  suffice. — Now,  Sir ; 
listen  to  me. 

You  are  living  on  a  Plane.  What  you  style  Flatland  is  the  vast 
level  surface  of  what  I  may  call  a  fluid,  on,  or  in,  the  top  of  which  you 
and  your  countrymen  move  about,  without  rising  above  it  or  falling 
below  it. 

I  am  not  a  plane  Figure,  but  a  Solid.  You  call  me  a  Circle ;  but  in 
reality  I  am  not  a  Circle,  but  an  infinite  number  of  Circles,  of  size 
varying  from  a  Point  to  a  Circle  of  thirteen  inches  in  diameter,  one 
placed  on  the  top  of  the  othen  When  I  cut  through  your  plane  as  I  am 
now  doing,  I  make  in  your  plane  a  section  which  you,  very  rightly, 
call  a  Circle.  For  even  a  Sphere — which  is  my  proper  name  in  my 
own  country — if  he  manifest  himself  at  all  to  an  inhabitant  of  Flatland — 
must  needs  manifest  himself  as  a  Circle. 


Flatland  7 1 

Do  you  not  remember — for  I,  who  see  all  things,  discerned  last  night 
the  phantasmal  vision  of  Lineland  written  upon  your  brain — do  you  not 
remember,  I  say,  how,  when  you  entered  the  realm  of  Lineland,  you  were 
compelled  to  manifest  yourself  to  the  King  not  as  a  Square,  but  as  a 
Line,  because  that  Linear  Realm  had  not  Dimensions  enough  to  represent 
the  whole  of  you,  but  only  a  slice  or  section  of  you  ?  In  precisely  the 
same  way,  your  country  of  Two  Dimensions  is  not  spacious  enough 
to  represent  me,  a  being  of  Three,  but  can  only  exhibit  a  slice  or  section 
of  me,  which  is  what  you  call  a  Circle. 

The  diminished  brightness  of  your  eye  indicates  incredulity.  But  now 
prepare  to  receive  proof  positive  of  the  truth  of  my  assertions.  You 
cannot  indeed  see  more  than  one  of  my  sections,  or  Circles,  at  a  time ; 
for  you  have  no  power  to  raise  your  eye  out  of  the  plane  of  Flatland ; 
but  you  can  at  least  see  that,  as  I  rise  in  Space,  so  my  section  becomes 
smaller.  See  now,  I  will  rise;  and  the  effect  upon  your  eye  will  be 
that  my  Circle  will  become  smaller  and  smaller  till  it  dwindles  to  a 
point  and  finally  vanishes. 


There  was  no  "rising"  that  I  could  see;  but  he  diminished  and 
finally  vanished.  I  winked  once  or  twice  to  make  sure  that  I  was  not 
dreaming.  But  it  was  no  dream.  For  from  the  depths  of  nowhere 
came  forth  a  hollow  voice — close  to  my  heart  it  seemed — "  Am  I  quite 


72  Flat  land 

gone?  Are  you  convinced  now?  Well,  now  I  will  gradually  return 
to  Flatland,  and  you  shall  see  my  section  become  larger  and  larger." 

Every  reader  in  Spaceland  will  easily  understand  that  my  mysterious 
Guest  was  speaking  the  language  of  truth  and  even  of  simplicity. 
But  to  me,  proficient  though  I  was  in  Flatland  Mathematics,  it  was  by 
no  means  a  simple  matter.  The  rough  diagram  given  above  will  make 
it  clear  to  any  Spaceland  child  that  the  Sphere,  ascending  in  the  three 
positions  indicated  there,  must  needs  have  manifested  himself  to  me, 
or  to  any  Flatlander,  as  a  Circle,  at  first  of  full  size,  then  small,  and 
at  last  very  small  indeed,  approaching  to  a  Point.  But  to  me,  although 
I  saw  the  facts  before  me,  the  causes  were  as  dark  as  ever.  All  that 
I  could  comprehend  was,  that  the  Circle  had  made  himself  smaller 
and  vanished,  and  that  he  had  now  reappeared  and  was  rapidly 
making  himself  larger. 

When  he  had  regained  his  original  size,  he  heaved  a  deep  sigh ;  for  he 
perceived  by  my  silence  that  I  had  altogether  failed  to  comprehend  him. 
And  indeed  I  was  now  inclining  to  the  belief  that  he  must  be  no  Circle 
at  all,  but  some  extremely  clever  juggler  ;  or  else  that  the  old  wives' 
tales  were  true,  and  that  after  all  there  were  such  people  as  Enchanters 
and  Magicians. 

After  a  long  pause  he  muttered  to  himself,  "One  resource  alone 
remains,  if  I  am  not  to  resort  to  action.  I  must  try  the  method  of 
Analogy."  Then  followed  a  still  longer  silence,  after  which  he  continued 
our  dialogue. 

SpJiere.  Tell  me,  Mr.  Mathematician ;  if  a  Point  moves  Northward, 
and  leaves  a  luminous  wake,  what  name  would  you  give  to  the  wake  ? 

/.  A  straight  Line. 

Sphere.  And  a  straight  Line  has  how  many  extremities  ? 

/.  Two. 

SpJiere.  Now  conceive   the  Northward  straight   line    moving    parallel 


Flatland 


73 


to  itself,  East  and  West,  so  that  every  point  in  it  leaves  behind  it  the 
wake  of  a  straight  Line.  What  name  will  you  give  to  the  Figure 
thereby  formed  ?  We  will  suppose  that  it  moves  through  a  distance 
equal  to  the  original  straight  Line. — What  name,  I  say  ? 

/.  A  Square. 

SpJiere.  And  how   many  sides  has  a  Square  ?    And  how  many  Angles  ? 

/.  Four  sides  and  four  angles. 

Sphere.  Now  stretch  your  imagination  a  little,  and  conceive  a 
Square  in  Flatland,  moving  parallel  to  itself  upward. 

/.  What?     Northward? 

Sphere.  No,   not  Northward  ;  upward ;  out   of  Flatland  altogether. 

If  it  moved  Northward,  the  Southern  points  in  the  Square  would 
have  to  move  through  the  positions  previously  occupied  by  the  Northern 
points.  But  that  is  not  my  meaning. 

I  mean  that  every  Point  in  you — for  you  are  a  Square  and  will  serve 
the  purpose  of  my  illustration — every  Point  in  you,  that  is  to  say  in 
what  you  call  your  inside,  is  to  pass  upwards  through  Space  in  such  a 
way  that  no  Point  shall  pass  through  the  position  previously  occupied 
by  any  other  Point ;  but  each  Point  shall  describe  a  straight  Line  of  its  own. 
This  is  all  in  accordance  with  Analogy ;  surely  it  must  be  clear  to  you. 

Restraining  my  impatience — for  I  was  now  under  a  strong  temptation 
to  rush  blindly  at  my  Visitor  and  to  precipitate  him  into  Space,  or  out 
of  Flatland,  anywhere,  so  that  I  could  get  rid  of  him — I  replied  : — 

"  And  what  may  be  the  nature  of  the  Figure  which  I  am  to  shape 
out  by  this  motion  which  you  are  pleased  to  denote  by  the  word 
'  upward  '  ?  I  presume  it  is  describable  in  the  language  of  Flatland." 

Sphere.  Oh,  certainly.  It  is  all  plain  and  simple,  and  in  strict 
accordance  with  Analogy — only,  by  the  way,  you  must  not  speak  of 
the  result  as  being  a  Figure,  but  as  a  Solid.  But  I  will  describe  it  to 
you.  Or  rather  not  I,  but  Analogy. 

F 


74 


Flatland 


We  began  with  a  single  Point,  which  of  course — being  itself  a  Point 
— has  only  one  terminal  Point. 

One  Point  produces  a  Line  with  two  terminal  Points. 

One  Line  produces  a  Square  with  four  terminal  Points. 

Now  you  can  yourself  give  the  answer  to  your  own  question  :  I,  2, 
4,  are  evidently  in  Geometrical  Progression.  What  is  the  next  number. 

/.  Eight. 

Sphere.  Exactly.  The  one  Square  produces  a  Something-which-you- 
do-not-as-yet-know-a-name-for-but-which-we-call-a-Cube  with  eight  terminal 
Points.  Now  are  you  convinced  ? 

/.  And  has  this  Creature  sides,  as  well  as  angles  or  what  you  call 
"  terminal  Points  ? " 

Sphere.  Of  course ;  and  all  according  to  Analogy.  But,  by  the 
way,  not  what  you  call  sides,  but  what  we  call  sides.  You  would  call 
them  solids. 

I.  And  how  many  solids  or  sides  will  appertain  to  this  Being  whom  I 
am  to  generate  by  the  motion  of  my  inside  in  an  "  upward  "  direction,  and 
whom  you  call  a  Cube  ? 

Sphere.  How  can  you  ask  ?  And  you  a  mathematician  !  The  side 
of  anything  is  always,  if  I  may  so  say,  one  Dimension  behind  the  thing. 
Consequently,  as  there  is  no  Dimension  behind  a  Point,  a  Point  has  o 
sides ;  a  Line,  if  I  may  so  say,  has  2  sides  (for  the  Points  of  a  Line  may 
be  called  by  courtesy,  its  sides)  ;  a  Square  has  4  sides  ;  o,  2,  4  ;  what 
Progression  do  you  call  that  ? 

/.  Arithmetical. 

Sphere.  And  what  is  the  next  number  ? 

/.  Six. 

Sphere.  Exactly.  Then  you  see  you  have  answered  your  own  question. 
The  Cube  which  you  will  generate  will  be  bounded  by  six  sides,  that  is  to 
say,  six  of  your  insides.  You  see  it  all  now,  eh  ? 


Flatland 


75 


"Monster,"  I  shrieked,  "be  thou  juggler,  enchanter,  dream,  or  devil,  no 
more  will  I  endure  thy  mockeries.  Either  thou  or  I  must  perish."  And 
saying  these  words  I  precipitated  myself  upon  him. 

§  17. — How  the  Sphere,  having  in  vain  tried  words,  resorted  to  deeds. 

It  was  in  vain.  I  brought  my  hardest  right  angle  into  violent  collision 
with  the  Stranger,  pressing  on  him  with  a  force  sufficient  to  have  destroyed 
any  ordinary  Circle :  but  I  could  feel  him  slowly  and  unarrestably  slipping 
from  my  contact ;  not  edging  to  the  right  nor  to  the  left,  but  moving 
somehow  out  of  the  world  and  vanishing  to  nothing.  Soon  there  was  a 
blank.  But  I  still  heard  the  Intruder's  voice. 

Sphere.  Why  will-  you  refuse  to  listen  to  reason  ?  I  had  hoped  to  find 
in  you — as  being  a  man  of  sense  and  an  accomplished  mathematician — a 
fit  apostle  for  the  Gospel  of  the  Three  Dimensions,  which  I  am  allowed  to 
preach  once  only  in  a  thousand  years  :  but  now  I  know  not  how  to  con- 
vince you.  Stay,  I  have  it.  Deeds,  and  not  words,  shall  proclaim  the 
truth.  Listen,  my  friend. 

I  have  told  you  I  can  see  from  my  position  in  Space  the  inside  of  all 
things  that  you  consider  closed.  For  example,  I  see  in  yonder  cupboard 
near  which  you  are  standing,  several  of  what  you  call  boxes  (but  like 
everything  else  in  Flatland,  they  have  no  tops  nor  bottoms)  full  of  money  ; 
I  see  also  two  tablets  of  accounts.  I  am  about  to  descend  into  that  cup- 
board and  to  bring  you  one  of  those  tablets.  I  saw  you  lock  the  cupboard 
half  an  hour  ago,  and  I  know  you  have  the  key  in  your  possession.  But  I 
descend  from  Space ;  the  doors,  you  see,  remain  unmoved.  Now  I  am  in 
the  cupboard  and  am  taking  the  tablet.  Now  I  have  it.  Now  I  ascend 
with  it. 

I  rushed  to  the  closet  and  dashed  the  door  open.  One  of  the  tablets 
was  gone.  With  a  mocking  laugh,  the  Stranger  appeared  in  the  other 

F   2 


j6  Flatland 

corner  of  the  room,  and  at  the  same  time  the  tablet  appeared  upon  the 
floor.  I  took  it  up.  There  could  be  no  doubt — it  was  the  missing 
tablet. 

I  groaned  with  horror,  doubting  whether  I  was  not  out  of  my  senses  ; 
but  the  Stranger  continued  :  "  Surely  you  must  now  see  that  my  explana- 
tion, and  no  other,  suits  the  phenomena  What  you  call  Solid  things  are 
really  superficial ;  what  you  call  Space  is  really  nothing  but  a  great  Plane. 
I  am  in  Space,  and  look  down  upon  the  insides  of  the  things  of  which  you 
only  see  the  outsides.  You  could  leave  this  Plane  yourself,  if  you  could 
but  summon  up  the  necessary  volition.  A  slight  upward  or  downward 
motion  would  enable  you  to  see  all  that  I  can  see. 

"  The  higher  I  mount,  and  the  further  I  go  from  your  Plane,  the  more  I 
can  see,  though  of  course  I  see  it  on  a  smaller  scale.  For  example,  I  am 
ascending  ;  now  I  can  see  your  neighbour  the  Hexagon  and  his  family  in 
their  several  apartments  ;  now  I  see  the  inside  of  the  Theatre,  ten  doors  off, 
from  which  the  audience  is  only  just  departing ;  and  on  the  other  side  a 
Circle  in  his  study,  sitting  at  his  books.  Now  I  shall  come  back  to  you. 
And,  as  a  crowning  proof,  what  do  you  say  to  my  giving  you  a  touch,  just 
the  least  touch,  in  your  stomach  ?  It  will  not  seriously  injure  you,  and  the 
slight  pain  you  may  suffer  cannot  be  compared  with  the  mental  benefit 
you  will  receive." 

Before  I  could  utter  a  word  of  remonstrance,  I  felt  a  shooting  pain  in 
my  inside,  and  a  demoniacal  laugh  seemed  to  issue  from  within  me.  A 
moment  afterwards  the  sharp  agony  had  ceased,  leaving  nothing  but  a  dull 
ache  behind,  and  the  Stranger  began  to  reappear,  saying,  as  he  gradually 
increased  in  size,  "  There,  I  have  not  hurt  you  much,  have  I  ?  If  you 
are  not  convinced  now,  I  don't  know  what  will  convince  you.  What 
say  you  ? " 

My  resolution  was  taken.  It  seemed  intolerable  that  I  should  endure 
existence  subject  to  the  arbitrary  visitations  of  a  Magician  who  could  thus 


Flat  land  77 

play  tricks  with  one's  very  stomach.  If  only  I  could  in  any  way  manage 
to  pin  him  against  the  wall  till  help  came  ! 

Once  more  I  dashed  my  hardest  angle  against  him,  at  the  same  time 
alarming  the  whole  household  by  my  cries  for  aid.  I  believe,  at  the 
moment  of  my  onset,  the  Stranger  had  sunk  below  our  Plane,  and  really 
found  difficulty  in  rising.  In  any  case  he  remained  motionless,  while  I, 
hearing,  as  I  thought,  the  sound  of  some  help  approaching,  pressed  against 
him  with  redoubled  vigour,  and  continued  to  shout  for  assistance. 

A  convulsive  shudder  ran  through  the  Sphere.  "  This  must  not  be," 
I  thought  I  heard  him  say ;  "  either  he  must  listen  to  reason,  or  I  must 
have  recourse  to  the  last  resource  of  civilization."  Then,  addressing  me 
in  a  louder  tone,  he  hurriedly  exclaimed,  "  Listen  :  no  stranger  must 
witness  what  you  have  witnessed.  Send  your  Wife  back  at  once,  before 
she  enters  the  apartment.  The  Gospel  of  Three  Dimensions  must  not 
be  thus  frustrated.  Not  thus  must  the  fruits  of  one  thousand  years  of 
waiting  be  thrown  away.  I  hear  her  coming.  Back !  back !  Away 
from  me,  or  you  must  go  with  me — whither  you  know  not — into  the 
Land  of  Three  Dimensions!" 

"  Fool !  Madman  !  Irregular  ! "  I  exclaimed  ;  "  never  will  I  release 
thee ;  thou  shalt  pay  the  penalty  of  thine  impostures." 

"  Ha !  Is  it  come  to  this  ? "  thundered  the  Stranger :  "  then  meet 
your  fate  :  out  of  your  Plane  you  go.  Once,  twice,  thrice !  'Tis  done ! " 

§  1 8. — How   I  came   to    Space  land,   and  what   I  saw   there. 

An  unspeakable  horror  seized  me.  There  was  a  darkness ;  then  a 
dizzy,  sickening  sensation  of  sight  that  was  not  like  seeing  ;  I  saw  a  Line 
that  was  no  Line  ;  Space  that  was  not  Space  ;  I  was  myself,  and  not  myself. 
When  I  could  find  voice,  I  shrieked  aloud  in  agony,  "  Either  this  is  mad- 
ness or  it  is  Hell."  "  It  is  neither,"  calmly  replied  the  voice  of  the  Sphere, 


jS  Flatland 

"it  is  Knowledge;  it  is  Three  Dimensions:  open  your  eye  once  again 
and  try  to  look  steadily." 

I  looked,  and,  behold,  a  new  world !  There  stood  before  me,  visibly 
incorporate,  all  that  I  had  before  inferred,  conjectured,  dreamed,  of  perfect 
Circular  beauty.  What  seemed  the  centre  of  the  Stranger's  form  lay 
open  to  my  view :  yet  I  could  see  no  heart,  nor  lungs,  nor  arteries,  only 
a  beautiful  harmonious  Something — for  which  I  had  no  words  ;  but  you, 
my  Readers  in  Spaceland,  would  call  it  the  surface  of  the  Sphere. 

Prostrating  myself  mentally  before  my  Guide,  I  cried,  "  How  is  it,  O 
divine  ideal  of  consummate  loveliness  and  wisdom,  that  I  see  thy  inside, 
and  yet  cannot  discern  thy  heart,  thy  lungs,  thy  arteries,  thy  liver?" 
"  What  you  think  you  see,  you  see  not,"  he  replied  ;  "  it  is  not  given  to 
you,  nor  to  any  other  Being,  to  behold  my  internal  parts.  I  am  of  a 
different  order  of  Beings  from  those  in  Flatland.  Were  I  a  Circle,  you 
could  discern  my  intestines,  but  I  am  a  Being  composed,  as  I  told  you 
before,  of  many  Circles,  the  Many  in  the  One,  called  in  this  country  a 
Sphere.  And,  just  as  the  outside  of  a  Cube  is  a  Square,  so  the  outside 
of  a  Sphere  presents  the  appearance  of  a  Circle." 

Bewildered  though  I  was  by  my  Teacher's  enigmatic  utterance,  I  no 
longer  chafed  against  it,  but  worshipped  him  in  silent  adoration.  He 
continued,  with  more  mildness  in  his  voice  :  "  Distress  not  yourself  if  you 
cannot  at  first  understand  the  deeper  mysteries  of  Spaceland.  By  degrees 
they  will  dawn  upon  you.  Let  us  begin  by  casting  back  a  glance  at  the 
region  whence  you  came.  Return  with  me  a  while  to  the  plains  of  Flat- 
land,  and  I  will  show  you  that  which  you  have  so  often  reasoned  and 
thought  about,  but  never  seen  with  the  sense  of  sight — a  visible  angle." 
"  Impossible ! "  I  cried  ;  but,  the  Sphere  leading  the  way,  I  followed  as  if 
in  a  dream,  till  once  more  his  voice  arrested  me :  "  Look  yonder,  and 
behold  your  own  Pentagonal  house  and  all  its  inmates." 

I  looked    below,  and  saw  with    my  physical    eye  all  that   domestic 


Flatland 


79 


individuality  which  I  had  hitherto  merely  inferred  with  the  understanding. 
And  how  poor  and  shadowy  was   the  inferred  conjecture  in  comparison 
with  the  reality  which  I   now  beheld  !     My  four  Sons  calmly  asleep  in  the 
North-Western 
rooms,  my  two 
orphan  Grand- 
sons     to     the 
South  ;         the 
Servants,     the 
Butler,     my 
Daughter,     all 
in  their  several 
apartments. 
Only  my  affec- 
tionate    Wife, 
alarmed  by  my 
continued    ab- 
sence, had  quit- 
ted her  room  and  was  roving  up  and  down  in  the  Hall,  anxiously  awaiting 
my  return.     Also  the  Page,  aroused  by  my  cries,  had  left  his  room,  and 
under  pretext  of  ascertaining  whether, I  had  fallen  somewhere  in  a  faint, 
was  prying  into  the  cabinet  in  my  study.     All  this  I  could  now  see,  not 
merely  infer  ;  and  as  we  came  nearer  and  nearer,  I  could  discern  even  the 
contents  of  my  cabinet,  and  the  two  chests  of  gold,  and  the  tablets  of 
which  the  Sphere  had  made  mention. 

Touched  by  my  Wife's  distress,  I  would  have  sprung  downward  to 
reassure  her,  but  I  found  myself  incapable  of  motion.  "  Trouble  not 
yourself  about  your  Wife,"  said  my  Guide ;  "  she  will  not  be  long  left  in 
anxiety  ;  meantime,  let  us  take  a  survey  of  Flatland." 

Once  more  I   felt  myself  rising  through    space.     It  was  even  as  the 


8o  Flatland 

Sphere  had  said.  The  further  we  receded  from  the  object  we  beheld,  the 
larger  became  the  field  of  vision.  My  native  city,  with  the  interior  of 
every  house  and  every  creature  therein,  lay  open  to  my  view  in  miniature. 
We  mounted  higher,  and  lo,  the  secrets  of  the  earth,  the  depths  of  mines 
and  inmost  caverns  of  the  hills,  were  bared  before  me. 

Awestruck  at  the  sight  of  the  mysteries  of  the  earth,  thus  unveiled 
before  my  unworthy  eye,  I  said  to  my  Companion,  "  Behold,  I  am  become 
as  a  God.  For  the  wise  men  in  our  country  say  that  to  see  ail  things,  or 
as  they  express  it,  omnividence,  is  the  attribute  of  God  alone."  There  was 
something  of  scorn  in  the  voice  of  my  Teacher  as  he  made  answer :  "  Is  it 
so  indeed  ?  Then  the  very  pickpockets  and  cut-throats  of  my  country  are 
to  be  worshipped  by  your  wise  men  as  being  Gods :  for  there  is  not  one  of 
them  that  does  not  see  as  much  as  you  see  now.  But  trust  me,  your  wise 
men  are  wrong." 

/.  Then  is  omnividence  the  attribute  of  others  beside  Gods  ? 

Sphere.  I  do  not  know.  But,  if  a  pick-pocket  or  a  cut-throat  -of  our 
country  can  see  everything  that  is  m  your  country,  surely  that  is  no  reason 
why  the  pick-pocket  or  cut-throat  should  be  accepted  by  you  as  a  God. 
This  omnividence,  as  you  call  it — it  is  not  a  common  word  in  Space- 
land — does  it  make  you  more  just,  more  merciful,  less  selfish,  more 
loving  ?  Not  in  the  least.  Then  how  does  it  make  you  more  divine  ? 

/.  "  More  merciful,  more  loving ! "  But  these  are  the  qualities  of 
women  !  And  we  know  that  a  Circle  is  a  higher  Being  than  a  Straight 
Line,  in  so  far  as  knowledge  and  wisdom  are  more  to  be  esteemed  than 
mere  affection. 

Sphere.  It  is  not  for  me  to  classify  human  faculties  according  to 
merit.  Yet  many  of  the  best  and  wisest  in  Spaceland  think  more  of  the 
affections  than  of  the  understanding,  more  of  your  despised  Straight  Lines 
than  of  your  belauded  Circles.  But  enough  of  this.  Look  yonder.  Do 
you  know  that  building  ? 


Flat  land  81 

I  looked,  and  afar  off  I  saw  an  immense  Polygonal  structure,  in  which 
I  recognized  the  General  Assembly  Hall  of  the  States  of  Flatland,  sur- 
rounded by  dense  lines  of  Pentagonal  buildings  at  right  angles  to  each 
other,  which  I  knew  to  be  streets  ;  and  I  perceived  that  I  was  approaching 
the  great  Metropolis. 

"  Here  we  descend,"  said  my  Guide.  It  was  now  morning,  the  first  hour 
of  the  first  day  of  the  two  thousandth  year  of  our  era.  Acting,  as  was 
their  wont,  in  strict  accordance  with  precedent,  the  highest  Circles  of  the 
realm  were  meeting  in  solemn  conclave,  as  they  had  met  on  the  first  hour 
of  the  first  day  of  the  year  1000,  and  also  on  the  first  hour  of  the  first 
day  of  the  year  o. 

The  minutes  of  the  previous  meetings  were  now  read  by  one  whom  I 
at  once  recognized  as  my  brother,  a  perfectly  Symmetrical  Square,  and 
the  Chief  Clerk  of  the  High  Council.  It  was  found  recorded  on  each 
occasion  that  :  "  Whereas  the  States  had  ^been  troubled  by  divers  ill-in- 
tentioned persons  pretending  to  hav«  received  revelations  from  another 
World,  and  professing  to  produce  demonstrations  whereby  they  had  insti- 
gated to  frenzy  both  themselves  and  others,  it  had  been  for  this  cause 
unanimously  resolved  by  the  Grand  Council  that  on  the  first  day  of  each 
millenary,  special  injunctions  be  sent  to  the  Prefects  in  the  several 
districts  of  Flatland,  to  make  strict  search  for  such  misguided  persons, 
and  without  formality'  of  mathematical  examination,  to  destroy  all  such 
as  were  Isosceles  of  any  degree,  to  scourge  and  imprison  any  regular 
Triangle,  to  cause  any  Square  or  Pentagon  to  be  sent  to  the  district 
Asylum,  and  to  arrest  any  one  of  higher  rank,  sending  him  straightway  to 
the  Capital  to  be  examined  and  judged  by  the  Council." 

"  You  hear  your  fate,"  said  the  Sphere  to  me,  while  the  Council  was 
passing  for  the  third  time  the  formal  resolution.  "  Death  or  imprisonment 
awaits  the  Apostle  of  the  Gospel  of  Three  Dimensions."  "  Not  so," 
replied  I,  "the  matter  is  now  so  clear  to  me,  the  nature  of  real  space  so 


82  Flatland 

palpable,  that  methinks  I  could  make  a  child  understand  it.  Permit  me 
but  to  descend  at  this  moment  and  enlighten  them."  "Not  yet,"  said 
my  Guide,  "  the  time  will  come  for  that.  Meantime  I  must  perform  my 
mission.  Stay  thou  there  in  thy  place."  Saying  these  words,  he  leaped 
with  great  dexterity  into  the  sea  (if  I  may  so  call  it)  of  Flatland,  right  in 
the  midst  of  the  ring  of  Counsellors.  "  I  come,"  cried  he,  "  to  proclaim 
that  there  is  a  land  of  Three  Dimensions." 

I  could  see  many  of  the  younger  Counsellors  start  back  in  manifest 
horror,  as  the  Sphere's  circular  section  widened  before  them.  But  on  a 
sign  from  the  presiding  Circle, — who  showed  not  the  slightest  alarm  or 
surprise — six  Isosceles  of  a  low  type  from  six  different  quarters  rushed 
upon  the  Sphere.  "  We  have  him,"  they  cried  ;  "  No  ;  yes  ;  we  have  him 
still !  he's  going  !  he's  gone  ! " 

"My  Lords,"  said  the  President  to  the  Junior  Circles  of  the  Council, 
"  there  is  not  the  slightest  need  for  surprise  ;  the  secret  archives,  to  which 
I  alone  have  access,  tell  me  that  a  similar  occurrence  happened  on  the 
last  two  millennial  commencements.  You  will,  of  course,  say  nothing  of 
these  trifles  outside  the  Cabinet." 

Raising  his  voice,  he  now  summoned  the  guard.  "  Arrest  the  police- 
men ;  gag  them.  You  know  your  duty."  After  he  had  consigned  to 
their  fate  the  wretched  policemen — ill-fated  and  unwilling  witnesses  of  a 
State-secret  which  they  were  not  to  be  permitted  to  reveal — he  again 
addressed  the  Counsellors.  "  My  Lords,  the  business  of  the  Council  being 
concluded,  I  have  only  to  wish  you  a  happy  New  Year."  Before  depart- 
ing, he  expressed,  at  some  length,  to  the  Clerk,  my  excellent  but  most 
unfortunate  brother,  his  sincere  regret  that,  in  accordance  with  precedent 
and  for  the  sake  of  secrecy,  he  must  condemn  him  to  perpetual  imprison- 
ment, but  added  his  satisfaction  that,  unless  some  mention  were  made  by 
him  of  that  day's  incident,  his  life  would  be  spared. 


Flatland 


§    19. — How,    though    the   Sphere   showed  me    other   mysteries   of 
Spaceland,  I  still  desired  more ;  and  what  came  of  it. 

When  I  saw  my  poor  brother  led  away  to  imprisonment,  I  attempted  to 
leap  down  into  the  Council  Chamber,  desiring  to  intercede  on  his  behalf, 
or  at  least  bid  him  farewell.  But  I  found  that  I  had  no  motion  of  my 
own.  I  absolutely  depended  on  the  volition  of  my  Guide,  who  said  in 
gloomy  tones,  "  Heed  not  thy  brother  ;  haply  thou  shalt  have  ample  time 
hereafter  to  condole  with  him.  Follow  me." 

Once  more  we  ascended  into  space.  "  Hitherto," 
said  the  Sphere,  "  I  have  shown  you  naught  save 
Plane  Figures  and  their  interiors.  Now  I  must 
introduce  you  to  Solids,  and  reveal  to  you  the  plan 
upon  which  they  are  constructed.  Behold  this 
multitude  of  moveable  square  cards.  See,  I  put 
one  on  another,  not,  as  you  supposed,  Northward 
of  the  other,  but  on  the  other.  Now  a  second, 
now  a  third.  See,  I  am  building  up  a  Solid  by 
a  multitude  of  Squares  parallel  to  one  another. 
Now  the  Solid  is  complete,  being  as  high  as  it  is 
long  and  broad,  and  we  call  it  a  Cube." 

"  Pardon  me,  my  Lord,"  replied  I  ;  "  but  to  my 
eye  the  appearance  is  as  of  an  Irregular  Figure 
whose  inside  is  laid  open  to  the  view ;  in  other 
words,  methinks  I  see  no  Solid,  but  a  Plane  such 

as   we  infer  in  Flatland  ;  only  of  an  Irregularity  which  betokens  some 
monstrous  criminal,  so  that  the  very  sight  of  it  is  painful  to  my  eyes." 

"  True,"  said  the  Sphere  ;  "  it  appears  to  you  a  Plane,  because  you 
are  not  accustomed  to  light  and  shade  and  perspective ;  just  as  in 


84  Flat  land 

Flatland  a  Hexagon  would  appear  a  Straight  Line  to  one  who  has 
not  the  Art  of  Sight  Recognition.  But  in  reality  it  is  a  Solid,  as  you 
shall  learn  by  the  sense  of  Feeling." 

He  then  introduced  me  to  the  Cube,  and  I  found  that  this  marvellous 
Being  was  indeed  no  Plane,  but  a  Solid ;  and  that  he  was  endowed  with 
six  plane  sides  and  eight  terminal  points  called  solid  angles ;  and  I  re- 
membered the  saying  of  the  Sphere  that  just  such  a  Creature  as  this 
would  be  formed  by  a  Square  moving,  in  Space,  parallel  to  himself :  and 
I  rejoiced  to  think  that  so  insignificant  a  Creature  as  I  could  in  some 
sense  be  called  the  Progenitor  of  so  illustrious  an  offspring. 

But  still  I  could  not  fully  understand  the  meaning  of  what  my 
Teacher  had  told  me  concerning  "  light "  and  "  shade  "  and  "  perspec- 
tive "  ;  and  I  did  not  hesitate  to  put  my  difficulties  before  him. 

Were  I  to  give  the  Sphere's  explanation  of  these  matters,  succinct 
and  clear  though  it  was,  it  would  be  tedious  to  an  inhabitant  of 
Space,  who  knows  these  things  already.  Suffice  it,  that  by  his  lucid 
statements,  and  by  changing  the  position  of  objects  and  lights,  and  by 
allowing  me  to  feel  the  several  objects  and  even  his  own  sacred 
Person,  he  at  last  made  all  things  clear  to  me,  so  that  I  could  now 
readily  distinguish  between  a  Circle  and  a  Sphere,  a  Plane  Figure 
and  a  Solid. 

This  was  the  Climax,  the  Paradise,  of  my  strange  eventful  History. 
Henceforth  I  have  to  relate  the  story  of  my  miserable  Fall: — most 
miserable,  yet  surely  most  undeserved  !  For  why  should  the  thirst  for 
knowledge  be  aroused,  only  to  be  disappointed  and  punished !  My 
volition  shrinks  from  the  painful  task  of  recalling  my  humiliation  ;  yet, 
like  a  second  Prometheus,  I  will  endure  this  and  worse,  if  by  any 
means  I  may  arouse  in  the  interiors  of  Plane  and  Solid  Humanity  a 
spirit  of  rebellion  against  the  Conceit  which  would  limit  our  Dimen- 
sions to  Two  or  Three  or  any  number  short  of  Infinity.  Away  then 


Flatland  85 

with  all  personal  considerations !  Let  me  continue  to  the  end,  as  I 
began,  without  further  digressions  or  anticipations,  pursuing  the  plain 
path  of  dispassionate  History.  The  exact  facts,  the  exact  words, — 
and  they  are  burnt  in  upon  my  brain, — shall  be  set  down  without 
alteration  of  an  iota  ;  and  let  my  Readers  judge  between  me  and 
Destiny. 

The  Sphere  would  willingly  have  continued  his  lessons  by  indoc- 
trinating me  in  the  conformation  of  all  regular  Solids,  Cylinders,  Cones, 
Pyramids,  Pentahedrons,  Hexahedrons,  Dodecahedrons  and  Spheres : 
but  I  ventured  to  interrupt  him.  Not  that  I  was  wearied  of  knowledge. 
On  the  contrary,  I  thirsted  for  yet  deeper  and  fuller  draughts  than 
he  was  offering  to  me. 

"  Pardon  me,"  said  I,  "  O  Thou  Whom  I  must  no  longer  address  as 
the  Perfection  of  all  Beauty ;  but  let  me  beg  thee  to  vouchsafe  thy 
servant  a  sight  of  thine  interior." 

Sphere.  "My  what?" 

/.  "  Thine  interior :  thy  stomach,  thy  intestines." 

Sphere.  "  Whence  this  ill-timed  impertinent  request  ?  And  what 
mean  you  by  saying  that  I  am  no  longer  the  Perfection  of  all 
Beauty  ? " 

/,  My  Lord,  your  own  wisdom  has  taught  me  to  aspire  to  One 
even  more  great,  more  beautiful,  and  more  closely  approximate  to 
Perfection  than  yourself.  As  you  yourself,  superior  to  all  Flatland 
forms,  combine  many  Circles  in  One,  so  doubtless  there  is  One  above 
you  who  combines  many  Spheres  in  One  Supreme  Existence,  sur- 
passing even  the  Solids  of  Spaceland.  And  even  as  we,  who  are  now 
in  Space,  look  down  on  Flatland  and  see  the  insides  of  all  things,  so 
of  a  certainty  there  is  yet  above  us  some  higher,  purer  region,  whither 
thou  dost  surely  purpose  to  lead  me — O  Thou  Whom  I  shall  always 
call,  everywhere  and  in  all  Dimensions,  my  Priest,  Philosopher,  and 


86  Flatland 

Friend — some  yet  more  spacious  Space,  some  more  dimensionable 
Dimensionality,  from  the  vantage-ground  of  which  we  shall  look  down 
together  upon  the  revealed  insides  of  Solid  things,  and  where  thine 
own  intestines,  and  those  of  thy  kindred  Spheres,  will  lie  exposed  to 
the  view  of  the  poor  wandering  exile  from  Flatland,  to  whom  so 
much  has  already  been  vouchsafed. 

Sphere.  Pooh!  Stuff!  Enough  of  this  trifling!  The  time  is  short, 
and  much  remains  to  be  done  before  you  are  fit  to  proclaim  the  Gospel  of 
Three  Dimensions  to  your  blind  benighted  countrymen  in  Flatland. 

/.  Nay,  gracious  Teacher,  deny  me  not  what  I  know  it  is  in  thy  power 
to  perform.  Grant  me  but  one  glimpse  of  thine  interior,  and  I  am  satisfied 
for  ever,  remaining  henceforth  thy  docile  pupil,  thy  unemancipable  slave, 
ready  to  receive  all  thy  teachings  and  to  feed  upon  the  words  that  fall 
from  thy  lips. 

Sphere.  Well,  then,  to  content  and  silence  you,  let  me  say  at  once,  I 
would  show  you  what  you  wish  if  I  could  ;  but  I  cannot.  Would  you 
have  me  turn  my  stomach  inside  out  to  oblige  you  ? 

7.  But  my  Lord  has  shown  me  the  intestines  of  all  my  countrymen  in 
the  Land  of  Two  Dimensions  by  taking  me  with  him  into  the  Land  of 
Three.  What  therefore  more  easy  than  now  to  take  his  servant  on  a 
second  journey  into  the  blessed  region  of  the  Fourth  Dimension,  where 
I  shall  look  down  with  him  once  more  upon  this  land  of  Three  Dimen- 
sions, and  see  the  inside  of  every  three-dimensioned  house,  the  secrets 
of  the  solid  earth,  the  treasures  of  the  mines  in  Spaceland,  and  the 
intestines  of  every  solid  living  creature,  even  of  the  noble  and  adorable 
Spheres. 

Sphere.  But  where  is  this  land  of  Four  Dimensions  ? 

/.  I  know  not :  but  doubtless  my  Teacher  knows. 

Sphere.  Not  I.  There  is  no  such  land.  The  very  idea  of  it  is  utterly 
inconceivable. 


Flatland  87 

/.  Your  Lordship  tempts  his  servant  to  see  whether  he  remembers  the 
revelations  imparted  to  him.  Trifle  not  with  me,  my  Lord  ;  I  crave,  I 
thirst,  for  more  knowledge.  Doubtless  we  cannot  see  that  other  higher 
Spaceland  now,  because  we  have  no  eye  in  our  stomachs.  But,  just  as 
there  was  the  realm  of  Flatland,  though  that  poor  puny  Lineland 
Monarch  could  neither  turn  to  left  nor  right  to  discern  it,  and  just  as  there 
was  close  at  hand,  and  touching  my  frame,  the  land  of  Three  Dimensions, 
though  I,  blind  senseless  wretch,  had  no  power  to  touch  it,  no  eye  in  my 
interior  to  discern  it,  so  of  a  surety  there  is  a  Fourth  Dimension,  which 
my  Lord  perceives  with  the  inner  eye  of  thought.  And  that  it  must  exist 
my  Lord  himself  has  taught  me.  Or  can  he  have  forgotten  what  he 
himself  imparted  to  his  servant  ? 

In  One  Dimension,  did  not  a  moving  Point  produce  a  Line  with  two 
terminal  points  ? 

In  Two  Dimensions,  did  not  a  moving  Line  produce  a  Square  with 
four  terminal  points  ? 

In  Three  Dimensions,  did  not  a  moving  Square  produce — did  not 
this  eye  of  mine  behold  it — that  blessed  Being,  a  Cube,  with  eight 
terminal  points  ? 

And  in  Four  Dimensions  shall  not  a  moving  Cube — alas,  for  Analogy, 
and  alas  for  the  Progress  of  Truth,  if  it  be  not  so — shall  not,  I  say,  the 
motion  of  a  divine  Cube  result  in  a  still  more  divine  Organization  with 
sixteen  terminal  points  ? 

Behold  the  infallible  confirmation  of  the  Series,  2,  4,  8,  16:  is  not  this 
a  Geometrical  Progression  ?  Is  not  this — if  I  might  quote  my  Lord's  own 
words — "  strictly  according  to  Analogy  "  ? 

Again,  was  I  not  taught  by  my  Lord  that  as  in  a  Line  there  are  two 
bounding  Points,  and  in  a  Square  there  are  four  bounding  Lines,  so  in  a 
Cube  there  must  be  six  bounding  Squares  ?  Behold  once  more  the  con- 
firming Series,  2,  4,  6 :  is  not  this  an  Arithmetical  Progression  ?  And 


88  Flatland 

consequently  does  it  not  of  necessity  follow  that  the  more  divine  offspring 
of  the  divine  Cube  in  the  Land  of  Four  Dimensions,  must  have  8  bounding 
Cubes :  and  is  not  this  also,  as  my  Lord  has  taught  me  to  believe,  "  strictly 
according  to  Analogy  "  ? 

O,  my  Lord,  my  Lord,  behold,  I  cast  myself  in  faith  upon  conjecture, 
not  knowing  the  facts;  and  I  appeal  to  your  Lordship  to  confirm  or  deny 
my  logical  anticipations.  If  I  am  wrong,  I  yield,  and  will  no  longer  demand 
a  Fourth  Dimension ;  but,  if  I  am  right,  my  Lord  will  listen  to  reason. 

I  ask  therefore,  is  it,  or  is  it  not,  the  fact,  that  ere  now  your  country- 
men also  have  witnessed  the  descent  of  Beings  of  a  higher  order  than 
their  own,  entering  closed  rooms,  even  as  your  Lordship  entered  mine, 
without  the  opening  of  doors  or  windows,  and  appearing  and  vanish- 
ing at  will  ?  On  the  reply  to  this  question  I  am  ready  to  stake  every- 
thing. Deny  it,  and  I  am  henceforth  silent.  Only  vouchsafe  an  answer. 

Sphere  (after  a  pause}.  It  is  reported  so.  But  men  are  divided  in 
opinion  as  to  the  facts.  And  even  granting  the  facts,  they  explain  them 
in  different  ways.  And  in  any  case,  however  great  may  be  the  number  of 
different  explanations,  no  one  has  adopted  or  suggested  the  theory  of  a 
Fourth  Dimension.  Therefore,  pray  have  done  with  this  trifling,  and  let 
us  return  to  business. 

/.  I  was  certain  of  it.  I  was  certain  that  my  anticipations  would  be 
fulfilled.  And  now  have  patience  with  me  and  answer  me  yet  one  more 
question,  best  of  Teachers !  Those  who  have  thus  appeared — no  one 
knows  whence — and  have  returned — no  one  knows  whither — have  they 
also  contracted  their  sections  and  vanished  somehow  into  that  more 
Spacious  Space,  whither  I  now  entreat  you  to  conduct  me  ? 

Spliere  (moodily].  They  have  vanished,  certainly — if  they  ever  ap- 
peared. But  most  people  say  that  these  visions  arose  from  the  thought — 
you  will  not  understand  me — from  the  brain  ;  from  the  perturbed  angularity 
of  the  Seer. 


Flatland  89 

7.  Say  they  so  ?  Oh,  believe  them  not.  Or  if  it  indeed  be  so,  that 
this  other  Space  is  really  Thoughtland,  then  take  me  to  that  blessed 
Region  where  I  in  Thought  shall  see  the  insides  of  all  solid  things. 
There,  before  my  ravished  eye,  a  Cube,  moving  in  some  altogether  new 
direction,  but  strictly  according  to  Analogy,  so  as  to  make  every  particle 
of  his  interior  pass  through  a  new  kind  of  Space  with  a  wake  of  its  own — 
shall  create  a  still  more  perfect  perfection  than  himself,  with  sixteen  terminal 
Extra-solid  angles,  and  Eight  solid  Cubes  for  his  Perimeter.  And  once 
there,  shall  we  stay  our  upward  course  ?  In  that  blessed  region  of  Four 
Dimensions,  shall  we  linger  on  the  threshold  of  the  Fifth,  and  not  enter 
therein  ?  Ah,  no !  Let  us  rather  resolve  that  our  ambition  shall  soar  with 
our  corporal  ascent.  Then,  yielding  to  our  intellectual  onset,  the  gates  of 
the  Sixth  Dimension  shall  fly  open ;  after  that  a  Seventh,  and  then 
an  Eighth 

How  long  I  should  have  continued  I  know  not.  In  vain  did  the 
Sphere,  in  his  voice  of  thunder,  reiterate  his  commands  of  silence,  and 
threaten  t  me  with  the  direst  penalties  if  I  persisted.  Nothing  could 
stem  the  flood  of  my  ecstatic  aspirations.  Perhaps  I  was  to  blame ; 
but  indeed  I  was  intoxicated  with  the  recent  draughts  of  Truth  to 
which  he  himself  had  introduced  me.  However,  the  end  was  not  long 
in  coming.  My  words  were  cut  short  by  a  crash  outside,  and  a 
simultaneous  crash  inside  me,  which  impelled  me  through  Space  with 
a  velocity  that  precluded  speech.  Down  !  down  !  down !  I  was  rapidly 
descending;  and  I  knew  that  return  to  Flatland  was  my  doom.  One 
glimpse,  one  last  and  never-to-be-forgotten  glimpse  I  had  of  that  dull 
level  wilderness — which  was  now  to  become  my  Universe  again — spread 
out  before  my  eye.  Then  a  darkness.  Then  a  final,  all-consummating 
thunder-peal ;  and,  when  I  came  to  myself,  I  was  once  more  a  common 
creeping  Square,  in  my  Study  at  home,  listening  to  the  Peace-Cry  of 
my  approaching  Wife. 

G 


90  Flatland 

§  20. — How   the   Sphere   encouraged  me   in    a  Vision. 

Although  I  had  less  than  a  minute  for  reflection,  I  felt,  by  a  kind 
of  instinct,  that  I  must  conceal  my  experiences  from  my  Wife.  Not 
that  I  apprehended,  at  the  moment,  any  danger  from  her  divulging 
my  secret,  but  I  know  that  to^any  Woman  in  Flatland  the  narrative 
of  my  adventures  must  needs  be  unintelligible.  So  I  endeavoured 
to  reassure  her  by  some  story,  invented  for  the  occasion,  that  I  had 
accidentally  fallen  through  the  trap-door  of  the  cellar,  and  had  there 
lain  stunned. 

The  Southward  attraction  in  our  country  is  so  slight  that  even  to 
a  Woman  my  tale  necessarily  appeared  extraordinary  and  well-nigh 
incredible ;  but  my  Wife,  whose  good  sense  far  exceeds  that  of 
the  average  of  her  Sex,  and  who  perceived  that  I  was  unusually 
excited,  did  not  argue  with  me  on  the  subject,  but  insisted  that  I  was 
ill  and  required  repose.  I  was  glad  of  an  excuse  for  retiring  to  my 
chamber  to  think  quietly  over  what  had  happened.  When  I  was  at 
last  by  myself,  a  drowsy  sensation  fell  on  me  ;  but  before  my  eyes 
closed  I  endeavoured  to  reproduce  the  Third  Dimension,  and  especially 
the  process  by  which  a  Cube  is  constructed  through  the  motion  of  a 
Square.  It  was  not  so  clear  as  I  could  have  wished ;  but  I  remembered 
that  it  must  be  "  Upward,  and  yet  not  Northward,"  and  I  determined 
steadfastly  to  retain  these  words  as  the  clue  which,  if  firmly  grasped, 
could  not  fail  to  guide  me  to  the  solution.  So  mechanically  repeating, 
like  a  charm,  the  words,  "Upward  yet  not  Northward,"  I  fell  into  a 
sound  refreshing  sleep. 

During  my  slumber  I  had  a  dream.  I  thought  I  was  once  more  by 
the  side  of  the  Sphere,  whose  lustrous  hue  betokened  that  he  had 
exchanged  his  wrath  against  me  for  perfect  placability.  We  were 
moving  together  towards  a  bright  but  infinitesimally  small  Point,  to 


Flat  land  91 

which  my  Master  directed  my  attention.  As  we  approached,  methought 
there  issued  from  it  a  slight  humming  noise  as  from  one  of  your 
Spaceland  blue-bottles,  only  less  resonant  by  far,  so  slight  indeed  that 
even  in  the  perfect  stillness  of  the  Vacuum  through  which  we  soared, 
the  sound  reached  not  our  ears  till  we  checked  our  flight  at  a  distance 
from  it  of  something  under  twenty  human  diagonals. 

"  Look  yonder,"  said  my  Guide,  "  in  Flatland  thou  hast  lived ; 
of  Lineland  thou  hast  received  a  vision  ;  thou  hast  soared  with  me  to 
the  heights  of  Spaceland;  now,  in  order  to  complete  the  range  of  thy 
experience,  I  conduct  thee  downward  to  the  lowest  depth  of  existence, 
even  to  the  realm  of  Pointland,  the  Abyss  of  No  Dimensions. 

"  Behold  yon  miserable  creature.  That  Point  is  a  Being  like 
ourselves,  but  confined  to  the  non-dimensional  Gulf.  He  is  himself 
his  own  World,  his  own  Universe;  of  any  other  than  himself  he  can 
form  no  conception  ;  he  knows  not  Length,  nor  Breadth,  nor  Height, 
for  he  has  had  no  experience  of  them  ;  he  has  no  cognizance  even  of 
the  number  Two  ;  nor  has  he  a  thought  of  Plurality ;  for  he  is  himself 
his  One  and  All,  being  really  Nothing.  Yet  mark  his  perfect  self- 
contentment,  and  hence  learn  this  lesson,  that  to  be  self-contented  is 
to  be  vile  and  ignorant,  and  that  to  aspire  is  better  than  to  be  blindly 
and  impotently  happy.  Now  listen." 

He  ceased  ;  and  there  arose  from  the  little  buzzing  creature  a  tiny, 
low,  monotonous,  but  distinct  tinkling,  as  from  one  of  your  Spaceland 
phonographs,  from  which  I  caught  these  words,  "  Infinite  beatitude  of 
existence  !  It  is  ;  and  there  is  none  else  beside  It." 

"What,"  said  I,  "does  the  puny  creature  mean  by  'it'?"  "He 
means  himself,"  said  the  Sphere :  "  have  you  not  noticed  before 
now,  that  babies  and  babyish  people  who  cannot  distinguish  themselves 
from  the  world,  speak  of  themselves  in  the  Third  Person  ?  But  hush ! " 

"  It  fills  all  Space,"  continued  the  little  soliloquizing  Creature,  "  and 


92  Flatland 

what  It  fills,  It  is.  What  It  thinks,  that  It  utters  ;  and  what  It  utters, 
that  It  hears ;  and  It  itself  is  Thinker,  Utterer,  Hearer,  Thought,  Word, 
Audition  ;  it  is  the  One,  and  yet  the  All  in  All.  Ah,  the  happiness, 
ah,  the  happiness  of  Being !  " 

"  Can  you  not  startle  the  little  thing  out  of  its  complacency  ? "  said 
I.  "  Tell  it  what  it  really  is,  as  you  told  me  ;  reveal  to  it  the  narrow 
limitations  of  Pointland,  and  lead  it  up  to  something  higher."  "  That  is 
no  easy  task,"  said  my  Master;  "try  you." 

Hereon,  raising  my  voice  to  the  uttermost,  I  addressed  the  Point 
as  follows : 

"  Silence,  silence,  contemptible  Creature.  You  call  yourself  the  All 
in  All,  but  you  are  the  Nothing :  your  so-called  Universe  is  a  mere  speck 
in  a  Line,  and  a  Line  is  a  mere  shadow  as  compared  with — "  "  Hush, 
hush,  you  have  said  enough,"  interrupted  the  Sphere,  "  now  listen,  and 
mark  the  effect  of  your  harangue  on  the  King  of  Pointland." 

The  lustre  of  the  Monarch,  who  beamed  more  brightly  than  ever 
upon  hearing  my  words,  showed  clearly  that  he  retained  his  com- 
placency ;  and  I  had  hardly  ceased  when  he  took  up  his  strain  again. 
"  Ah,  the  joy,  ah,  the  joy  of  Thought !  What  can  It  not  achieve  by 
thinking !  Its  own  Thought  coming  to  Itself,  suggestive  of  Its  dis- 
paragement, thereby  to  enhance  Its  happiness  !  Sweet  rebellion  stirred 
up  to  result  in  triumph !  Ah,  the  divine  creative  power  of  the  All 
in  One!  Ah,  the  joy,  the  joy  of  Being!  " 

"You  see,"  said  my  Teacher,  "how  little  your  words  have  done. 
So  far  as  the  Monarch  understands  them  at  all,  he  accepts  them  as 
his  own — for  he  cannot  conceive  of  any  other  except  himself — and  plumes 
himself  upon  the  variety  of  '  Its  Thought '  as  an  instance  of  creative 
Power.  Let  us  leave  this  God  of  Pointland  to  the  ignorant  fruition  of  his 
omnipresence  and  omniscience :  nothing  that  you  or  I  can  do  can  rescue 
him  from  his  self-satisfaction." 


Flatland 


93 


After  this,  as  we  floated  gently  back  to  Flatland,  I  could  hear  the 
mild  voice  of  my  Companion  pointing  the  moral  of  my  vision,  and 
stimulating  me  to  aspire,  and  to  teach  others  to  aspire.  He  had  been 
angered  at  first — he  confessed — by  my  ambition  to  soar  to  Dimensions 
above  the  Third  ;  but,  since  then,  he  had  received  fresh  insight,  and  he  was 
not  too  proud  to  acknowledge  his  error  to  a  Pupil.  Then  he  proceeded 
to  initiate  me  into  mysteries  yet  higher  than  those  I  had  witnessed, 
showing  me  how  to  construct  Extra-Solids  by  the  motion  of  Solids,  and 
Double  Extra-Solids  by  the  motion  of  Extra-Solids,  and  all  "strictly 
according  to  Analogy,"  all  by  methods  so  simple,  so  easy,  as  to  be 
patent  even  to  the  Female  Sex. 

§  21. — How  I  tried  to   teach   the   theory    of  Three   Dimensions 
to   my    Grandson,  and  with   what   success. 

I  awoke  rejoicing,  and  began  to  reflect  on  the  glorious  career  before 
me.  I  would  go  forth,  methought,  at  once,  and  evangelize  the  whole 
of  Flatland.  Even  to  Women  and  Soldiers  should  the  Gospel  of  Three 
Dimensions  be  proclaimed.  I  would  begin  with  my  Wife. 

Just  as  I  had  decided  on  the  plan  of  my  operations,  I  heard  the 
sound  of  many  voices  in  the  street  commanding  silence.  Then  followed 
a  louder  voice.  It  was  a  herald's  proclamation.  Listening  attentively, 
I  recognized  the  words  of  the  Resolution  of  the  Council,  enjoining  the 
arrest,  imprisonment,  or  execution  of  any  one  who  should  pervert  the 
minds  of  the  people  by  delusions,  and  by  professing  to  have  received 
revelations  from  another  World. 

I  reflected.  This  danger  was  not  to  be  trifled  with.  It  would  be 
better  to  avoid  it  by  omitting  all  mention  of  my  Revelation,  and  by 
proceeding  on  the  path  of  Demonstration — which  after  all,  seemed  so 
simple  and  so  conclusive  that  nothing  would  be  lost  by  discarding  the 


94  Flatland 

former  means.  "  Upward,  not  Northward  " — was  the  clue  to  the  whole 
proof.  It  had  seemed  to  me  fairly  clear  before  I  fell  asleep  ;  and  when 
I  first  awoke,  fresh  from  my  dream,  it  had  appeared  as  patent  as 
Arithmetic ;  but  somehow  it  did  not  seem  to  me  quite  so  obvious  now. 
Though  my  Wife  entered  the  room  opportunely  just  at  that  moment,  I 
decided,  after  we  had  interchanged  a  few  words  of  commonplace 
conversation,  not  to  begin  with  her. 

My  Pentagonal  Sons  were  men  of  character  and  standing,  and 
physicians  of  no  mean  reputation,  but  not  great  in  mathematics,  and,  in 
that  respect,  unfit  for  my  purpose.  But  it  occurred  to  me  that  a  young 
and  docile  Hexagon,  with  a  mathematical  turn,  would  be  a  most  suitable 
pupil.  Why  therefore  not  make  my  first  experiment  with  my  little 
precocious  Grandson,  whose  casual  remarks  on  the  meaning  of  33  had  met 
with  the  approval  of  the  Sphere  ?  Discussing  the  matter  with  him,  a 
mere  boy,  I  should  be  in  perfect  safety  ;  for  he  would  know  nothing  of 
the  Proclamation  of  the  Council ;  whereas  I  could  not  feel  sure  that  my 
Sons — so  greatly  did  their  patriotism  and  reverence  for  the  Circles  pre- 
dominate over  mere  blind  affection — might  not  feel  compelled  to  hand 
me  over  to  the  Prefect,  if  they  found  me  seriously  maintaining  the 
seditious  heresy  of  the  Third  Dimension. 

But  the  first  thing  to  be  done  was  to  satisfy  in  some  way  the 
curiosity  of  my  Wife,  who  naturally  wished  to  know  something  of  the 
reasons  for  which  the  Circle  had  desired  that  mysterious  interview,  and 
of  the  means  by  which  he  had  entered  our  house.  Without  entering 
into  the  details  of  the  elaborate  account  I  gave  her, — an  account,  I  fear, 
not  quite  so  consistent  with  truth  as  my  Readers  in  Spaceland  might 
desire, —  I  must  be  content  with  saying  that  I  succeeded  at  last 
in  persuading  her  to  return  quietly  to  her  household  duties  without 
eliciting  from  me  any  reference  to  the  World  of  Three  Dimensions. 
This  done,  I  immediately  sent  for  my  Grandson  ;  for,  to  confess  the 


Flatland  95 

truth,  I  felt  that  all  that  I  had  seen  and  heard  was  in  some  strange  way 
slipping  away  from  me,  like  the  image  of  a  half-grasped,  tantalizing 
dream,  and  I  longed  to  essay  my  skill  in  making  a  first  disciple. 

When  my  Grandson  entered  the  room  I  carefully  secured  the  door. 
Then,  sitting  down  by  his  side  and  taking  our  mathematical  tablets — or, 
as  you  would  call  them,  Lines — I  told  him  we  would  resume  the  lesson 
of  yesterday.  I  taught  him  once  more  how  a  Point  by  motion  in  One 
Dimension  produces  a  Line,  and  how  a  straight  Line  in  Two  Dimensions 
produces  a  Square.  After  this,  forcing  a  laugh,  I  said,  "  And  now,  you 
scamp,  you  wanted  to  make  me  believe  that  a  Square  may  in  the  same  way 
by  motion  '  Upward,  not  Northward,'  produce  another  figure,  a  sort  of 
extra  Square  in  Three  Dimensions.  Say  that  again,  you  young  rascal." 

At  this  moment  we  heard  once  more  the  herald's  "  O  yes !  O  yes ! " 
outside  in  the  street  proclaiming  the  Resolution  of  the  Council.  Young 
though  he  was,  my  Grandson — who  was  unusually  intelligent  for  his  age, 
and  bred  up  in  perfect  reverence  for  the  authority  of  the  Circles — 
took  in  the  situation  with  an  acuteness  for  which  I  was  quite  unprepared. 
He  remained  silent  till  the  last  words  of  the  Proclamation  had  died  away, 
and  then,  bursting  into  tears,  "  Dear  Grandpapa,"  he  said,  "  that  was 
only  my  fun,  and  of  course  I  meant  nothing  at  all  by  it  ;  and  we  did 
not  know  anything  then  about  the  new  Law ;  and  I  don't  think  I  said 
anything  about  the  Third  Dimension  ;  and  I  am  sure  I  did  not  say  one 
word  about  '  Upward,  not  Northward,'  for  that  would  be  such  nonsense, 
you  know.  How  could  a  thing  move  Upward,  and  not  Northward  ? 
Upward,  and  not  Northward  !  Even  if  I  were  a  baby,  I  could  not  be 
so  absurd  as  that.  How  silly  it  is  !  Ha !  ha  !  ha !  " 

"  Not  at  all  silly,"  said  I,  losing  my  temper  ;  "  here  for  example,  I 
take  this  Square," — and,  at  the  word,  I  grasped  a  moveable  Square, 
which  was  lying  at  hand — "  and  I  move  it,  you  see,  not  Northward  but 
— yes,  I  move  it  Upward — that  is  to  say,  not  Northward,  but  I  move  it 


96  Flatland 

somewhere — not  exactly  like  this,  but  somehow—  Here  I  brought  my 
sentence  to  an  inane  conclusion,  shaking  the  Square  about  in  a  purpose- 
less manner,  much  to  the  amusement  of  my  Grandson,  who  burst  out 
laughing  louder  than  ever,  and  declared  that  I  was  not  teaching  him, 
but  joking  with  him ;  and  so  saying  he  unlocked  the  door  and  ran 
out  of  the  room.  Thus  ended  my  first  attempt  to  convert  a  pupil  to 
the  Gospel  of  Three  Dimensions. 

§  22. — How   I  then   tried  to   diffuse   the    Theory    of  Three 
Dimensions   by   other   means,   and  of  the   result. 

My  failure  with  my  Grandson  did  not  encourage  me  to  communicate 
my  secret  to  others  of  my  household  ;  yet  neither  was  I  led  by  it  to 
despair  of  success.  Only  I  saw  that  I  must  not  wholly  rely  on  the  catch- 
phrase  "  Upward,  not  Northward,"  but  must  rather  endeavour  to  seek  a 
demonstration  by  setting  before  the  public  a  clear  view  of  the  whole 
subject ;  and  for  this  purpose  it  seemed  necessary  to  resort  to  writing. 

So  I  devoted  several  months  in  privacy  to  the  composition  of  a  treatise 
on  the  mysteries  of  Three  Dimensions.  Only,  with  the  view  of  evading 
the  Law,  if  possible,  I  spoke  not  of  a  physical  Dimension,  but  of  a 
Thoughtland  whence,  in  theory,  a  Figure  could  look  down  upon  Flatland 
and  see  simultaneously  the  insides  of  all  things,  and  where  it  was 
possible  that  there  might  be  supposed  to  exist  a  Figure  environed,  as  it 
were,  with  six  Squares,  and  containing  eight  terminal  Points.  But  in 
writing  this  book  I  found  myself  sadly  hampered  by  the  impossibility 
of  drawing  such  diagrams  as  were  necessary  for  my  purpose ;  for  of 
course,  in  our  country  of  Flatland,  there  are  no  tablets  but  Lines,  and 
no  diagrams  but  Lines,  all  in  one  straight  Line  and  only  distinguishable 
by  difference  of  size  and  brightness ;  so  that,  when  I  had  finished  my 
treatise  (which  I  entitled  "  Through  Flatland  to  Thoughtland ")  I  could 
not  feel  certain  that  many  would  understand  my  meaning. 


Flatland  97 

Meanwhile  ray  life  was  under  a  cloud.  All  pleasures  palled  upon 
me  ;  all  sights  tantalized  and  tempted  me  to  outspoken  treason,  because 
I  could  not  but  compare  what  I  saw  in  Two  Dimensions  with  what  it 
really  was  if  seen  in  Three,  and  could  hardly  refrain  from  making  my 
comparisons  aloud.  I  neglected  my  clients  and  my  own  business  to  give 
myself  to  the  contemplation  of  the  mysteries  which  I  had  once  beheld, 
yet  which  I  could  impart  to  no  one,  and  found  daily  more  difficult  to 
reproduce  even  before  my  own  mental  vision. 

One  day,  about  eleven  months  after  my  return  from  Spaceland,  I 
tried  to  see  a  Cube  with  my  eye  closed,  but  failed ;  and  though  I  succeeded 
afterwards,  I  was  not  then  quite  certain  (nor  have  I  been  ever  afterwards) 
that  I  had  exactly  realized  the  original.  This  made  me  more  ,melancholy 
than  before,  and  determined  me  to  take  some  step  ;  yet  what,  I  knew  not. 
I  felt  that  I  would  have  been  willing  to  sacrifice  my  life  for  the  Cause, 
if  thereby  I  could  have  produced  conviction.  But  if  I  could  not  convince 
my  Grandson,  how  could  I  convince  the  highest  and  most  developed 
Circles  in  the  land  ? 

And  yet  at  times  my  spirit  was  too  strong  for  me,  and  I  gave  vent  to 
dangerous  utterances.  Already  I  was  considered  heterodox  if  not 
treasonable,  and  I  was  keenly  alive  to  the  dangers  of  my  position  ; 
nevertheless  I  could  not  at  times  refrain  from  bursting  out  into  suspicious 
or  half-seditious  utterances,  even  among  the  highest  Polygonal  and 
Circular  society.  When,  for  example,  the  question  arose  about  the 
treatment  of  those  lunatics  who  said  that  they  had  received  the  power  of 
seeing  the  insides  of  things,  I  would  quote  the  saying  of  an  ancient  Circle, 
who  declared  that  prophets  and  inspired  people  are  always  considered  by 
the  majority  to  be  mad ;  and  I  could  not  help  occasionally  dropping  such 
expressions  as  "  the  eye  that  discerns  the  interiors  of  things,"  and  "  the 
all-seeing  land  : "  once  or  twice  I  even  let  fall  the  forbidden  terms  "  the 
Third  and  Fourth  Dimensions."  At  last,  to  complete  a  series  of  minor 

H 


98  Flatland 

indiscretions,  at  a  meeting  of  our  Local  Speculative  Society  held  at  the 
palace  of  the  Prefect  himself, — some  extremely  silly  person  having  read  an 
elaborate  paper  exhibiting  the  precise  reasons  why  Providence  has  limited 
the  number  of  Dimensions  to  Two,  and  why  the  attribute  of  omnividence 
is  assigned  to  the  Supreme  alone^I  so  far  forgot  myself  as  to  give  an 
exact  account  of  the  whole  of  my  voyage  with  the  Sphere  into  Space,  and 
to  the  Assembly  Hall  in  our  Metropolis,  and  then  to  Space  again,  and  of 
my  return  home,  and  of  everything  that  I  had  seen  and  heard  in  fact  or 
vision.  At  first,  indeed,  I  pretended  that  I  was  describing  the  imaginary 
experiences  of  a  fictitious  person  ;  but  my  enthusiasm  soon  forced  me  to 
throw  off  all  disguise,  and  finally,  in  a  fervent  peroration,  I  exhorted  all 
my  hearers  to  divest  themselves  of  prejudice  and  to  become  believers  in 
the  Third  Dimension. 

Need  I  say  that  I  was  at  once  arrested  and  taken  before  the  Council  ? 

Next  morning,  standing  in  the  very  place  where  but  a  very  few  months 
ago  the  Sphere  had  stood  in  my  company,  I  was  allowed  to  begin  and  to 
continue  my  narration  unquestioned  and  uninterrupted.  But  from  the  first 
I  foresaw  my  fate  ;  for  the  President,  noting  that  a  guard  of  the  better  sort 
of  Policemen  was  in  attendance,  of  angularity  little,  if  at  all,  under  55°, 
ordered  them  to  be  relieved  before  I  began  my  defence,  by  an  inferior 
class  of  2°  or  3°.  I  knew  only  too  well  what  that  meant.  I  was  to  be 
executed  or  imprisoned,  and  my  story  was  to  be  kept  secret  from  the 
world  by  the  simultaneous  destruction  of  the  officials  who  had  heard  it ; 
and,  this  being  the  case,  the  President  desired  to  substitute  the  cheaper  for 
the  more  expensive  victims. 

After  I  had  concluded  my  defence,  the  President,  perhaps  perceiving 
that  some  of  the  junior  Circles  had  been  moved  by  my  evident  earnestness, 
asked  me  two  questions  : — 

i.  Whether  I  could  indicate  the  direction  which  I  meant  when  I  used 
the  words  "  Upward,  not  Northward  "  ? 


Flatland  99 

2.  Whether  I  could  by  any  diagrams  or  descriptions  (other  than  the 
enumeration  of  imaginary  sides  and  angles)  indicate  the  Figure  I  was 
pleased  to  call  a  Cube? 

I  declared  that  I  could  say  nothing  more,  and  that  I  must  commit 
myself  to  the  Truth,  whose  cause  would  surely  prevail  in  the  end. 

The  President  replied  that  he  quite  concurred  in  my  sentiment,  and 
that  I  could  not  do  better.  I  must  be  sentenced  to  perpetual  imprison- 
ment ;  but  if  the  Truth  intended  that  I  should  emerge  from  prison  and 
evangelize  the  world,  the  Truth  might  be  trusted  to  bring  that  result  to 
pass.  Meanwhile  I  should  be  subjected  to  no  discomfort  that  was  not 
necessary  to  preclude  escape,  and,  unless  I  forfeited  the  privilege  by 
misconduct,  I  should  be  occasionally  permitted  to  see  my  brother,  who 
had  preceded  me  to  my  prison. 

Seven  years  have  elapsed  and  I  am  still  a  prisoner,  and — if  I  except 
the  occasional  visits  of  my  brother — debarred  from  all  companionship  save 
that  of  my  jailers.  My  brother  is  one  of  the  best  of  Squares,  just,  sensible, 
cheerful,  and  not  without  fraternal  affection  ;  yet  I  must  confess  that  my 
weekly  interviews,  at  least  in  one  respect,  cause  me  the  bitterest  pain. 
He  was  present  when  the  Sphere  manifested  himself  in  the  Council 
Chamber  ;  he  saw  the  Sphere's  changing  sections ;  he  heard  the  ex- 
planation of  the  phenomena  then  given  to  the  Circles.  Since  that  time, 
scarcely  a  week  has  passed  during  seven  whole  years,  without  his  hearing 
from  me  a  repetition  of  the  part  I  played  in  that  manifestation,  together 
with  ample  descriptions  of  all  the  phenomena  in  Spaceland,  and  the 
arguments  for  the  existence  of  Solid  things  derivable  from  Analogy. 
Yet — I  take  shame  to  be  forced  to  confess  it — my  brother  has  not  yet 
grasped  the  nature  of  the  Third  Dimension,  and  frankly  avows  his 
disbelief  in  the  existence  of  a  Sphere. 

Hence  I  am  absolutely  destitute  of  converts,  and,  for  aught  that  I 
can  see,  the  millennial  Revelation  has  been  made  to  me  for  nothing. 


ioo  Flat  land 

Prometheus  up  in  Spaceland  was  bound  for  bringing  down  fire  for 
mortals,  but  I — poor  Flatland  Prometheus — lie  here  in  prison  for  bring- 
ing down  nothing  to  my  countrymen.  Yet  I  exist  in  the  hope  that 
these  memoirs,  in  some  manner,  I  know  not  how,  may  find  their  way  to 
the  minds  of  humanity  in  Some  Dimension,  and  may  stir  up  a  race  of 
rebels  who  shall  refuse  to  be  confined  to  limited  Dimensionality. 

That  is  the  hope  of  my  brighter  moments.  Alas,  it  is  not  always  so. 
Heavily  weighs  on  me  at  times  the  burdensome  reflection  that  I  cannot 
honestly  say  I  am  confident  as  to  the  exact  shape  of  the  once-seen,  oft- 
regretted  Cube ;  and  in  my  nightly  visions  the  mysterious  precept, 
"  Upward,  not  Northward,"  haunts  me  like  a  soul-devouring  Sphinx.  It 
is  part  of  the  martyrdom  which  I  endure  for  the  cause  of  the  Truth  that 
there  are  seasons  of  mental  weakness,  when  Cubes  and  Spheres  flit  away 
into  the  background  of  scarce-possible  existences ;  when  the  Land  of 
Three  Dimensions  seems  almost  as  visionary  as  the  Land  of  One  or 
None  ;  nay,  when  even  this  hard  wall  that  bars  me  from  my  freedom,  these 
very  tablets  on  which  I  am  writing,  and  all  the  substantial  realities  of 
Flatland  itself,  appear  no  better  than  the  offspring  of  a  diseased  imagination, 
or  the  baseless  fabric  of  a  dream. 


LONDON:  R.  CLAY,  SONS,  AND  TAYLOR,  PRINTERS. 


J